{"id":30434,"date":"2026-10-29T08:23:44","date_gmt":"2026-10-29T08:23:44","guid":{"rendered":"https:\/\/blog.oratrics.com\/?p=30434"},"modified":"2026-10-29T10:38:41","modified_gmt":"2026-10-29T10:38:41","slug":"area-of-triangle","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/area-of-triangle\/","title":{"rendered":"What Is the Area of a Triangle? Formulas, Examples &amp; How to Find Missing Sides"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"30434\" class=\"elementor elementor-30434\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d5c7026 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"d5c7026\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b8dc922\" data-id=\"b8dc922\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-28bcde1\" data-id=\"28bcde1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d0a1486 elementor-widget elementor-widget-heading\" data-id=\"d0a1486\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">What Is the Area of a Triangle? Formulas, Examples &amp; How to Find Missing Sides<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5e5056 elementor-widget elementor-widget-text-editor\" data-id=\"b5e5056\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">The area of triangle is the amount of flat space enclosed by its three sides. The basic triangle area formula is <\/span><b>A = \u00bd \u00d7 base \u00d7 height<\/b><span style=\"font-weight: 400;\">. If you want to know how to calculate the area of a triangle, start there, then pick a different formula when the question gives other information.<\/span><\/p><p><span style=\"font-weight: 400;\">Triangle area matters in geometry and everyday life: roofs, sails, garden beds and land plots are triangles or can be cut into them. This guide covers every common method, step-by-step examples, how to find the side of a triangle from its area, and a short practice set.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13d8796 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"13d8796\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/demo.oratrics.com\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Book a Free Demo Today<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f6290a elementor-widget elementor-widget-image\" data-id=\"1f6290a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"647\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration-1024x647.webp\" class=\"attachment-large size-large wp-image-30466\" alt=\"explaining the area of triangle with a geometric triangle diagram showing its base, perpendicular height, and measurement lines on graph paper\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration-1024x647.webp 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration-300x190.webp 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration-768x486.webp 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration-1536x971.webp 1536w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Scalene-Triangle-Area-Illustration.webp 1577w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-d54e954\" data-id=\"d54e954\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d348421 elementor-widget elementor-widget-html\" data-id=\"d348421\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Poppins:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\r\n\r\n<div class=\"toc-wrapper\">\r\n    \r\n    \r\n    <div class=\"custom-toc\" id=\"custom-toc\">\r\n        <div class=\"toc-title\">\r\n            \u2630 Table of Contents\r\n        <\/div>\r\n        <ul class=\"toc-list\" id=\"toc-list\"><\/ul>\r\n    <\/div>\r\n    \r\n<\/div>\r\n\r\n<style>\r\n\/* Parent Fixed Wrapper holding both components together *\/\r\n.toc-wrapper {\r\n    position: fixed;\r\n    top: 150px; 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Meaning and Definition\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c8e2bfd elementor-widget elementor-widget-text-editor\" data-id=\"c8e2bfd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">The area of a triangle is the measure of the region enclosed by its three sides. It equals half the base multiplied by the perpendicular height, and it is written in square units such as cm\u00b2 or m\u00b2.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Base (b):<\/b><span style=\"font-weight: 400;\"> the side you measure from.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Height (h):<\/b><span style=\"font-weight: 400;\"> the perpendicular distance from the base to the opposite vertex. A slanted side is not the height unless it is perpendicular to the base.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Area counts unit squares inside the shape, so a length in cm becomes cm \u00d7 cm = cm\u00b2.<\/span><\/p><p><b>Example:<\/b><span style=\"font-weight: 400;\"> base 10 cm, height 6 cm gives \u00bd \u00d7 10 \u00d7 6 = <\/span><b>30 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8ba7bf8\" data-id=\"8ba7bf8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fe49ce5 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"fe49ce5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4e7244d\" data-id=\"4e7244d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-79a0e65\" data-id=\"79a0e65\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b3816b7 elementor-widget elementor-widget-heading\" data-id=\"b3816b7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle Formula \u2013 Basic Formula Explained<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-88753c1 elementor-widget elementor-widget-text-editor\" data-id=\"88753c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>A = \u00bd \u00d7 b \u00d7 h<\/b><span style=\"font-weight: 400;\">, where A is the area, b is the base and h is the perpendicular height.<\/span><\/p><p><span style=\"font-weight: 400;\">Picture triangle ABC with BC as the base. Drop a dotted line from A that meets BC at D with a right-angle mark. AD is the height. In an obtuse triangle D falls on the extension of the base, but AD is still perpendicular. Any side can be the base, as long as you use its matching height.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0a0b0db\" data-id=\"0a0b0db\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-995aceb elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"995aceb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-53d9f29\" data-id=\"53d9f29\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-16a1ef8\" data-id=\"16a1ef8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0bf2b4f elementor-widget elementor-widget-heading\" data-id=\"0bf2b4f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">How to Find Area of Triangle Step by Step\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b7664c9 elementor-widget elementor-widget-text-editor\" data-id=\"b7664c9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Identify the base.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find the perpendicular height.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply base by height.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Divide by 2.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Write the answer in square units.<\/span><\/li><\/ol><p><b>Example 1:<\/b><span style=\"font-weight: 400;\"> b = 8 cm, h = 5 cm: 40 \u00f7 2 = <\/span><b>20 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 2:<\/b><span style=\"font-weight: 400;\"> b = 12 m, h = 7.5 m: 90 \u00f7 2 = <\/span><b>45 m\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 3:<\/b><span style=\"font-weight: 400;\"> b = 15 cm, h = 9 cm: 135 \u00f7 2 = <\/span><b>67.5 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c1feaf8\" data-id=\"c1feaf8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-41199c5 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"41199c5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4635ed9\" data-id=\"4635ed9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5ba7644\" data-id=\"5ba7644\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dbf4e03 elementor-widget elementor-widget-heading\" data-id=\"dbf4e03\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Formula of Area of Triangle for Different Types\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df89d63 elementor-widget elementor-widget-text-editor\" data-id=\"df89d63\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h3>Area of a Right-Angled Triangle<\/h3><p><span style=\"font-weight: 400;\">A = \u00bd \u00d7 leg\u2081 \u00d7 leg\u2082. The legs are perpendicular, so one is the base and the other the height. Legs 6 cm and 8 cm give <\/span><b>24 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3>Area of an Equilateral Triangle<\/h3><p><span style=\"font-weight: 400;\">A = (\u221a3\/4) a\u00b2. Side 10 cm gives (\u221a3\/4) \u00d7 100 = 25\u221a3 \u2248 <\/span><b>43.30 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3>Area of an Isosceles Triangle<\/h3><p><span style=\"font-weight: 400;\">Find the height h = \u221a(a\u00b2 \u2212 b\u00b2\/4), where a is each equal side and b the base, then use \u00bd b h. Equal sides 13 cm, base 10 cm: h = \u221a(169 \u2212 25) = 12, so A = \u00bd \u00d7 10 \u00d7 12 = <\/span><b>60 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3>Area of a Scalene Triangle<\/h3><p><span style=\"font-weight: 400;\">No single shortcut exists. Use \u00bd b h if a height is given, Heron&#8217;s formula for three sides, or \u00bd ab sin C for two sides and the included angle. Sides 13, 14, 15 cm give <\/span><b>84 cm\u00b2<\/b><span style=\"font-weight: 400;\"> (see Heron&#8217;s formula below).<\/span><\/p><table><tbody><tr><td><p><b>Triangle<\/b><\/p><\/td><td><p><b>Formula<\/b><\/p><\/td><td><p><b>Use when<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Any<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd b h<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Base and height known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Right-angled<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd \u00d7 leg\u2081 \u00d7 leg\u2082<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Both legs known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Equilateral<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">(\u221a3\/4) a\u00b2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Side known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Isosceles<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd b \u221a(a\u00b2 \u2212 b\u00b2\/4)<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Equal side and base known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Scalene<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Heron&#8217;s formula<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Three sides known<\/span><\/p><\/td><\/tr><\/tbody><\/table>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-2c1552f\" data-id=\"2c1552f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-04135e2 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"04135e2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7f65f0d\" data-id=\"7f65f0d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6911d4e\" data-id=\"6911d4e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8316dac elementor-widget elementor-widget-heading\" data-id=\"8316dac\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle with 3 Sides \u2013 Heron's Formula\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8677f6c elementor-widget elementor-widget-text-editor\" data-id=\"8677f6c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">When all three sides are known but the height is not, use <\/span><b>Heron&#8217;s formula<\/b><span style=\"font-weight: 400;\">:<\/span><\/p><p><b>A = \u221a[s(s \u2212 a)(s \u2212 b)(s \u2212 c)]<\/b><span style=\"font-weight: 400;\">, where <\/span><b>s = (a + b + c)\/2<\/b><\/p><p><span style=\"font-weight: 400;\">Here a, b, c are the side lengths and s is the semi-perimeter, half the perimeter. The sides must satisfy the triangle inequality: any two sides must add to more than the third. Sides 2, 3, 7 fail because 2 + 3 &lt; 7.<\/span><\/p><p><b>Example 1:<\/b><span style=\"font-weight: 400;\"> sides 5, 12, 13 cm. s = 15. A = \u221a(15 \u00d7 10 \u00d7 3 \u00d7 2) = \u221a900 = <\/span><b>30 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 2:<\/b><span style=\"font-weight: 400;\"> sides 7, 8, 9 cm. s = 12. A = \u221a(12 \u00d7 5 \u00d7 4 \u00d7 3) = \u221a720 = 12\u221a5 \u2248 <\/span><b>26.83 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 3 (harder):<\/b><span style=\"font-weight: 400;\"> sides 25, 29, 36 m. s = 45. A = \u221a(45 \u00d7 20 \u00d7 16 \u00d7 9) = \u221a129600 = <\/span><b>360 m\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5d50c6c\" data-id=\"5d50c6c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3b61f80 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"3b61f80\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-448e8b9\" data-id=\"448e8b9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0a04124\" data-id=\"0a04124\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1f782ad elementor-widget elementor-widget-heading\" data-id=\"1f782ad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle Equilateral \u2013 Formula and Examples\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3295449 elementor-widget elementor-widget-text-editor\" data-id=\"3295449\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>A = (\u221a3\/4) a\u00b2.<\/b><span style=\"font-weight: 400;\"> All three sides equal a. <\/span><b>Derivation:<\/b><span style=\"font-weight: 400;\"> the altitude splits the triangle into two right triangles with hypotenuse a and base a\/2, so h = \u221a(a\u00b2 \u2212 a\u00b2\/4) = (\u221a3\/2) a. Then A = \u00bd \u00d7 a \u00d7 (\u221a3\/2) a = (\u221a3\/4) a\u00b2.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Side 6 cm: 9\u221a3 \u2248 <\/span><b>15.59 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Side 2.5 cm: 1.5625\u221a3 \u2248 <\/span><b>2.71 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">The exact value is 9\u221a3; 15.59 is a rounded approximation.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7d4d4ea\" data-id=\"7d4d4ea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-26ab9ec elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"26ab9ec\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-90b14ad\" data-id=\"90b14ad\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-089aa39\" data-id=\"089aa39\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-faf09e7 elementor-widget elementor-widget-heading\" data-id=\"faf09e7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle in Coordinate Geometry<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2feafb4 elementor-widget elementor-widget-text-editor\" data-id=\"2feafb4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">For vertices A(x\u2081, y\u2081), B(x\u2082, y\u2082), C(x\u2083, y\u2083):<\/span><\/p><p><b>A = \u00bd |x\u2081(y\u2082 \u2212 y\u2083) + x\u2082(y\u2083 \u2212 y\u2081) + x\u2083(y\u2081 \u2212 y\u2082)|<\/b><\/p><p><span style=\"font-weight: 400;\">Plot the three points on a coordinate plane and join them. The absolute value is needed because listing the points clockwise gives a negative sum, and area cannot be negative. If the area is 0, the points are collinear.<\/span><\/p><p><b>Example 1:<\/b><span style=\"font-weight: 400;\"> A(1, 1), B(5, 1), C(3, 5). Sum = 1(\u22124) + 5(4) + 3(0) = 16, so A = <\/span><b>8 square units<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 2:<\/b><span style=\"font-weight: 400;\"> A(2, 3), B(\u22121, 4), C(4, \u22122). Sum = 2(6) + (\u22121)(\u22125) + 4(\u22121) = 13, so A = <\/span><b>6.5 square units<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-76f4e9d\" data-id=\"76f4e9d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ec7378c elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"ec7378c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8e2107b\" data-id=\"8e2107b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4510c73\" data-id=\"4510c73\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-63fef5d elementor-widget elementor-widget-heading\" data-id=\"63fef5d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle in Vector Form\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6c3f1d elementor-widget elementor-widget-text-editor\" data-id=\"c6c3f1d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">If <\/span><b>a<\/b><span style=\"font-weight: 400;\"> and <\/span><b>b<\/b><span style=\"font-weight: 400;\"> are side vectors from the same vertex, <\/span><b>A = \u00bd |a \u00d7 b|<\/b><span style=\"font-weight: 400;\">. The cross product&#8217;s magnitude is |a||b| sin \u03b8, the area of the parallelogram on a and b, and a triangle is half of it.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>2D:<\/b><span style=\"font-weight: 400;\"> a = (4, 0), b = (1, 3). a \u00d7 b = 4\u00d73 \u2212 0\u00d71 = 12, so A = <\/span><b>6<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>3D:<\/b><span style=\"font-weight: 400;\"> a = (1, 2, 3), b = (2, 1, 0). a \u00d7 b = (\u22123, 6, \u22123), magnitude \u221a54 = 3\u221a6, so A = 3\u221a6\/2 \u2248 <\/span><b>3.67<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-567e54b\" data-id=\"567e54b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3759217 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"3759217\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-dc0ca44\" data-id=\"dc0ca44\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-65bc323\" data-id=\"65bc323\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6c0c014 elementor-widget elementor-widget-heading\" data-id=\"6c0c014\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">How to Find the Side of a Triangle Using Its Area\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cd93ba0 elementor-widget elementor-widget-text-editor\" data-id=\"cd93ba0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Important:<\/b><span style=\"font-weight: 400;\"> area alone does not fix the sides of a general triangle. Base 6 with height 4 and base 8 with height 3 both give area 12. You need extra information.<\/span><\/p><h3>Finding the Base When Area and Height Are Known<\/h3><p><b>Base = 2 \u00d7 Area \/ Height.<\/b><span style=\"font-weight: 400;\"> Area 36 cm\u00b2, height 9 cm: base = 72\/9 = <\/span><b>8 cm<\/b><span style=\"font-weight: 400;\">. Area 52.5 m\u00b2, height 7 m: base = 105\/7 = <\/span><b>15 m<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3>Finding the Height When Area and Base Are Known<\/h3><p><b>Height = 2 \u00d7 Area \/ Base.<\/b><span style=\"font-weight: 400;\"> Area 60 cm\u00b2, base 15 cm: height = <\/span><b>8 cm<\/b><span style=\"font-weight: 400;\">. Area 45 cm\u00b2, base 12 cm: height = <\/span><b>7.5 cm<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3>Finding the Side of an Equilateral Triangle from Its Area<\/h3><p><b>a = \u221a(4A\/\u221a3).<\/b><span style=\"font-weight: 400;\"> Area 16\u221a3 cm\u00b2: a\u00b2 = 64, so a = <\/span><b>8 cm<\/b><span style=\"font-weight: 400;\">. Here the area is enough because the shape has one free measurement.<\/span><\/p><h3>Finding a Missing Side Using the Pythagorean Theorem<\/h3><p><span style=\"font-weight: 400;\">In a right-angled triangle, hypotenuse\u00b2 = leg\u00b2 + leg\u00b2. Hypotenuse 17, one leg 8: other leg = \u221a(289 \u2212 64) = \u221a225 = <\/span><b>15<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f897dcd\" data-id=\"f897dcd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-94e6067 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"94e6067\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-74ca8aa\" data-id=\"74ca8aa\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-988e674\" data-id=\"988e674\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d0372db elementor-widget elementor-widget-heading\" data-id=\"d0372db\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle Using Two Sides and an Included Angle\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d4e2e9f elementor-widget elementor-widget-text-editor\" data-id=\"d4e2e9f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>A = \u00bd ab sin C<\/b><span style=\"font-weight: 400;\">, where C is the angle between sides a and b. It helps when the height is not given.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">a = 8, b = 10, C = 30\u00b0: \u00bd \u00d7 80 \u00d7 0.5 = <\/span><b>20 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">a = 7, b = 9, C = 60\u00b0: \u00bd \u00d7 63 \u00d7 (\u221a3\/2) = 63\u221a3\/4 \u2248 <\/span><b>27.28 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-dbe360c\" data-id=\"dbe360c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d74859b elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"d74859b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e0ec5d1\" data-id=\"e0ec5d1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ec79713\" data-id=\"ec79713\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8d382e elementor-widget elementor-widget-heading\" data-id=\"a8d382e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle \u2013 All Important Formulas at a Glance\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51dd35a elementor-widget elementor-widget-text-editor\" data-id=\"51dd35a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<table><tbody><tr><td><p><b>Given<\/b><\/p><\/td><td><p><b>Formula<\/b><\/p><\/td><td><p><b>When to use<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Base, height<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd b h<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Perpendicular height known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Right-angled<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd leg\u2081 leg\u2082<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Both legs known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Equilateral<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">(\u221a3\/4) a\u00b2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Side known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Three sides<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u221a[s(s\u2212a)(s\u2212b)(s\u2212c)]<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Height unknown<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Two sides, included angle<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd ab sin C<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Angle between the sides<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Coordinates<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd |x\u2081(y\u2082\u2212y\u2083)+x\u2082(y\u2083\u2212y\u2081)+x\u2083(y\u2081\u2212y\u2082)|<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Points on a plane<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Vectors<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd |a \u00d7 b|<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Two side vectors<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Missing base<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2A \/ h<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Area, height known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Missing height<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2A \/ b<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Area, base known<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Equilateral side<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u221a(4A\/\u221a3)<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Area known<\/span><\/p><\/td><\/tr><\/tbody><\/table>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-2fde37b\" data-id=\"2fde37b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-481c8d9 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"481c8d9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0c1a7d5\" data-id=\"0c1a7d5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0eda7ec\" data-id=\"0eda7ec\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7a4f683 elementor-widget elementor-widget-heading\" data-id=\"7a4f683\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Solved Examples on Area of Triangle\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55f4709 elementor-widget elementor-widget-text-editor\" data-id=\"55f4709\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Isosceles:<\/b><span style=\"font-weight: 400;\"> equal sides 10 cm, base 12 cm. h = \u221a(100 \u2212 36) = 8, so A = \u00bd \u00d7 12 \u00d7 8 = <\/span><b>48 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Heron&#8217;s:<\/b><span style=\"font-weight: 400;\"> sides 11, 13, 20 cm. s = 22, A = \u221a(22 \u00d7 11 \u00d7 9 \u00d7 2) = \u221a4356 = <\/span><b>66 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Coordinates:<\/b><span style=\"font-weight: 400;\"> A(\u22122, 1), B(4, 3), C(1, \u22124). Sum = \u221214 \u2212 20 \u2212 2 = \u221236, so A = \u00bd \u00d7 36 = <\/span><b>18 square units<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Missing base:<\/b><span style=\"font-weight: 400;\"> area 84 cm\u00b2, height 12 cm. Base = 168\/12 = <\/span><b>14 cm<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Word problem:<\/b><span style=\"font-weight: 400;\"> a triangular garden has base 18 m and height 10 m, and seed costs \u20b940 per m\u00b2. Area = 90 m\u00b2, cost = <\/span><b>\u20b93,600<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Word problem:<\/b><span style=\"font-weight: 400;\"> a triangular gable wall is 8 m wide and 3 m high. Area = <\/span><b>12 m\u00b2<\/b><span style=\"font-weight: 400;\">; at 4 m\u00b2 per litre, one coat needs <\/span><b>3 litres<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ba98a9c\" data-id=\"ba98a9c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-38120dd elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"38120dd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-bc5e8ec\" data-id=\"bc5e8ec\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9834af9\" data-id=\"9834af9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3ca1f56 elementor-widget elementor-widget-heading\" data-id=\"3ca1f56\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Common Mistakes While Calculating the Area of a Triangle<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5bf065e elementor-widget elementor-widget-text-editor\" data-id=\"5bf065e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Forgetting \u00bd:<\/b><span style=\"font-weight: 400;\"> b = 10, h = 6 gives 30, not 60.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Using the slanted side:<\/b><span style=\"font-weight: 400;\"> base 10, slant 13, height 12 gives \u00bd \u00d7 10 \u00d7 12 = 60, not 65.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Mixed units:<\/b><span style=\"font-weight: 400;\"> base 2 m and height 50 cm: convert to 0.5 m, so A = 0.5 m\u00b2.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Missing square units:<\/b><span style=\"font-weight: 400;\"> write 24 cm\u00b2, not 24 cm.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Wrong s in Heron&#8217;s formula:<\/b><span style=\"font-weight: 400;\"> for 3, 4, 5 use s = 6, not the perimeter 12.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Dropping the absolute value:<\/b><span style=\"font-weight: 400;\"> a sum of \u221236 gives area 18.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Assuming area fixes the sides:<\/b><span style=\"font-weight: 400;\"> area 12 fits many triangles.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-abc0acc\" data-id=\"abc0acc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ea1c327 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"ea1c327\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6363be6\" data-id=\"6363be6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4204a46\" data-id=\"4204a46\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2b21f11 elementor-widget elementor-widget-heading\" data-id=\"2b21f11\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Easy Tricks to Remember Triangle Area Formulas<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b94329b elementor-widget elementor-widget-text-editor\" data-id=\"b94329b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Two identical triangles form a parallelogram, so a triangle is half of base \u00d7 height.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Always draw the perpendicular height first.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Match the formula to the given information using the table above.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Estimate to check: base 10, height 6 sits inside a 10 \u00d7 6 rectangle, so the area must be under 60.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-179b390\" data-id=\"179b390\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ee6b780 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"ee6b780\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-2150523\" data-id=\"2150523\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-345ecdc\" data-id=\"345ecdc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2fa2a03 elementor-widget elementor-widget-heading\" data-id=\"2fa2a03\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Area of Triangle Practice Questions with Answers<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d6fd83e elementor-widget elementor-widget-text-editor\" data-id=\"d6fd83e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Easy<\/b><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Base 10 cm, height 7 cm. Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area 48 cm\u00b2, height 8 cm. Find the base.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Right triangle with legs 5 cm and 12 cm. Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Equilateral triangle, side 12 cm. Find the area.<\/span><\/li><\/ol><p><b>Intermediate<\/b><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Sides 8, 15, 17 cm. Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Isosceles, equal sides 17 cm, base 16 cm. Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Right triangle, hypotenuse 25 cm, one leg 7 cm. Find the other leg and the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area 64 cm\u00b2, base twice the height. Find both.<\/span><\/li><\/ol><p><b>Advanced<\/b><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Vertices (0, 0), (8, 0), (3, 6). Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Show (1, 2), (4, 6), (7, 10) are collinear.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Side vectors (5, 2) and (1, 4). Find the area.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Sides 12 cm and 9 cm with included angle 30\u00b0. Find the area.<\/span><\/li><\/ol><p><b>Answers:<\/b><span style=\"font-weight: 400;\"> (1) 35 cm\u00b2. (2) 12 cm. (3) 30 cm\u00b2. (4) 36\u221a3 \u2248 62.35 cm\u00b2. (5) s = 20, \u221a3600 = 60 cm\u00b2. (6) h = 15, area 120 cm\u00b2. (7) Leg 24 cm, area 84 cm\u00b2. (8) h\u00b2 = 64, so height 8 cm, base 16 cm. (9) 24 square units. (10) The sum is \u22124 + 32 \u2212 28 = 0, so the area is 0 and the points are collinear. (11) \u00bd(5\u00d74 \u2212 2\u00d71) = 9 square units. (12) \u00bd \u00d7 12 \u00d7 9 \u00d7 0.5 = 27 cm\u00b2.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5a9ad24\" data-id=\"5a9ad24\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-06e3672 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"06e3672\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-84a4429\" data-id=\"84a4429\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-df234be\" data-id=\"df234be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-caf2cca elementor-widget elementor-widget-heading\" data-id=\"caf2cca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e07d541 elementor-widget elementor-widget-text-editor\" data-id=\"e07d541\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">The area of a triangle is the space inside its sides, measured in square units. Remember A = \u00bd \u00d7 base \u00d7 height first, then choose Heron&#8217;s formula, the trigonometric formula, or the coordinate and vector methods depending on what you are given. Work through the practice questions and check each answer.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-fe7849e\" data-id=\"fe7849e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-73f5b8a elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"73f5b8a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-647357f\" data-id=\"647357f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-bedb7e6\" data-id=\"bedb7e6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59d840a elementor-widget elementor-widget-heading\" data-id=\"59d840a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d5f680b elementor-widget elementor-widget-accordion\" data-id=\"d5f680b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2241\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2241\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What is the formula of area of triangle?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2241\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2241\"><p><span style=\"font-weight: 400;\">A = \u00bd \u00d7 base \u00d7 height, with the height perpendicular to the base.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2242\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2242\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How do you find the area of a triangle with three sides?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2242\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2242\"><p><span style=\"font-weight: 400;\">Use Heron&#8217;s formula: find s = (a + b + c)\/2, then A = \u221a[s(s \u2212 a)(s \u2212 b)(s \u2212 c)].<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2243\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2243\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How do you find the area of an equilateral triangle?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2243\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2243\"><p><span style=\"font-weight: 400;\">Use A = (\u221a3\/4) a\u00b2, where a is the side length.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2244\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-2244\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How do you find the area of a right-angled triangle?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2244\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-2244\"><p><span style=\"font-weight: 400;\">Multiply the two legs and divide by 2.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2245\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-2245\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What is the vector formula?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2245\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-2245\"><p><span style=\"font-weight: 400;\">A = \u00bd |a \u00d7 b| for two side vectors from the same vertex.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2246\" class=\"elementor-tab-title\" data-tab=\"6\" role=\"button\" aria-controls=\"elementor-tab-content-2246\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Can you find the sides if only the area is known?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2246\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"6\" role=\"region\" aria-labelledby=\"elementor-tab-title-2246\"><p><span style=\"font-weight: 400;\">Not for a general triangle, since many triangles share one area. An equilateral triangle is the exception.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2247\" class=\"elementor-tab-title\" data-tab=\"7\" role=\"button\" aria-controls=\"elementor-tab-content-2247\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How do you find the area without the height?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2247\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"7\" role=\"region\" aria-labelledby=\"elementor-tab-title-2247\"><p><span style=\"font-weight: 400;\">Use Heron&#8217;s formula for three sides, or \u00bd ab sin C for two sides and the included angle.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What is the formula of area of triangle?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">A = \\u00bd \\u00d7 base \\u00d7 height, with the height perpendicular to the base.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How do you find the area of a triangle with three sides?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Use Heron&#8217;s formula: find s = (a + b + c)\\\/2, then A = \\u221a[s(s \\u2212 a)(s \\u2212 b)(s \\u2212 c)].<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How do you find the area of an equilateral triangle?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Use A = (\\u221a3\\\/4) a\\u00b2, where a is the side length.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How do you find the area of a right-angled triangle?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Multiply the two legs and divide by 2.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"What is the vector formula?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">A = \\u00bd |a \\u00d7 b| for two side vectors from the same vertex.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Can you find the sides if only the area is known?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Not for a general triangle, since many triangles share one area. 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Formulas, Examples &amp; How to Find Missing Sides The area of triangle is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30466,"comment_status":"open","ping_status":"open","sticky":false,"template":"rttpg_full_width","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[9],"tags":[],"class_list":["post-30434","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-explorer-program"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Area of Triangle : Formulas, Examples &amp; 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