{"id":31412,"date":"2026-11-03T09:06:59","date_gmt":"2026-11-03T09:06:59","guid":{"rendered":"https:\/\/blog.oratrics.com\/?p=31412"},"modified":"2026-11-03T11:07:45","modified_gmt":"2026-11-03T11:07:45","slug":"trapezoid","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/trapezoid\/","title":{"rendered":"Trapezoid: Shape, Properties, Area Formula and Easy Examples"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"31412\" class=\"elementor elementor-31412\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-786c9c4 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"786c9c4\" 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-878010c\" data-id=\"878010c\" 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-bd30a50\" data-id=\"bd30a50\" 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-b9ee7cf elementor-widget elementor-widget-heading\" data-id=\"b9ee7cf\" 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\">Trapezoid: Shape, Properties, Area Formula and Easy Examples<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7cfc301 elementor-widget elementor-widget-text-editor\" data-id=\"7cfc301\" 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;\">A trapezoid is a flat shape with four straight sides. In the most common school definition, it has <\/span><b>one pair of parallel sides<\/b><span style=\"font-weight: 400;\">. Parallel sides are sides that never meet, no matter how far you extend them.<\/span><\/p><p><span style=\"font-weight: 400;\">The two parallel sides are called the <\/span><b>bases<\/b><span style=\"font-weight: 400;\">. The other two sides are called the <\/span><b>legs<\/b><span style=\"font-weight: 400;\">. The distance between the two bases is called the <\/span><b>height<\/b><span style=\"font-weight: 400;\">. You can see this shape in many places around you. A bucket, a handbag, a bridge support, and a lampshade often look like a trapezoid.<\/span><\/p><p><span style=\"font-weight: 400;\">So, if someone asks, &#8220;what is trapezoid in maths?&#8221;, here is a short answer: it is a four-sided shape (a quadrilateral) with at least one pair of parallel sides.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-506f16b elementor-align-center elementor-widget elementor-widget-button\" data-id=\"506f16b\" 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-248d0e0 elementor-widget elementor-widget-image\" data-id=\"248d0e0\" 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=\"576\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover-1024x576.webp\" class=\"attachment-large size-large wp-image-31400\" alt=\"Maths Worksheet for Class 1 with Practice questions and Answers\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover-1024x576.webp 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover-300x169.webp 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover-768x432.webp 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover-1536x864.webp 1536w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Class-1-Maths-Worksheet-Cover.webp 1672w\" 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-3c1d3fd\" data-id=\"3c1d3fd\" 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-1a7fa05 elementor-widget elementor-widget-html\" data-id=\"1a7fa05\" 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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\r\n        overflow-y: visible;\r\n    }\r\n\r\n    .custom-toc .toc-title {\r\n        font-size: 25px;\r\n    }\r\n\r\n    .custom-toc .toc-list a {\r\n        font-size: 14px;\r\n    }\r\n}\r\n<\/style>\r\n\r\n<script>\r\ndocument.addEventListener(\"DOMContentLoaded\", function () {\r\n    const tocList = document.getElementById(\"toc-list\");\r\n    const h1 = document.querySelector(\"h1\");\r\n    const h2s = document.querySelectorAll(\"h2\");\r\n\r\n    function createId(text) {\r\n        return text.toLowerCase().replace(\/[^a-z0-9]+\/g, '-');\r\n    }\r\n\r\n    if (h1) {\r\n        if (!h1.id) {\r\n            h1.id = createId(h1.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.innerHTML = `<a href=\"#${h1.id}\">${h1.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    }\r\n\r\n    h2s.forEach(h2 => {\r\n        if (!h2.id) {\r\n            h2.id = createId(h2.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.classList.add(\"toc-h2\");\r\n        li.innerHTML = `<a href=\"#${h2.id}\">${h2.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    });\r\n});\r\n<\/script>\t\t\t\t<\/div>\n\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-6770b2a elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"6770b2a\" 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-c84facf\" data-id=\"c84facf\" 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-ad430eb\" data-id=\"ad430eb\" 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-6735a28 elementor-widget elementor-widget-heading\" data-id=\"6735a28\" 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\">Trapezoid Shape: Main Parts<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-992848b elementor-widget elementor-widget-text-editor\" data-id=\"992848b\" 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;\">Before you learn any formula, it helps to know the parts of the trapezoid shape.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Base 1 (a):<\/b><span style=\"font-weight: 400;\"> The top parallel side.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Base 2 (b):<\/b><span style=\"font-weight: 400;\"> The bottom parallel side.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Legs (c and d):<\/b><span style=\"font-weight: 400;\"> The two slanted sides.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Height (h):<\/b><span style=\"font-weight: 400;\"> The straight, vertical distance between the two bases. It makes a right angle (90\u00b0) with both bases.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Median (m):<\/b><span style=\"font-weight: 400;\"> A line that joins the midpoints of the two legs. It is parallel to the bases.<\/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-efdf2c4\" data-id=\"efdf2c4\" 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-5aebe01 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"5aebe01\" 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-304374b\" data-id=\"304374b\" 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-e9e5e86\" data-id=\"e9e5e86\" 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-1759cc5 elementor-widget elementor-widget-heading\" data-id=\"1759cc5\" 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\">Difference Between Trapezium and Trapezoid<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6956eb7 elementor-widget elementor-widget-text-editor\" data-id=\"6956eb7\" 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;\">Many students get confused here, and it is a very common question. The difference between trapezium and trapezoid depends on <\/span><b>which country&#8217;s English you use<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><table><tbody><tr><td><p><b>Term<\/b><\/p><\/td><td><p><b>In the US and Canada<\/b><\/p><\/td><td><p><b>In the UK, India, Australia and most other countries<\/b><\/p><\/td><\/tr><tr><td><p><b>Trapezoid<\/b><\/p><\/td><td><p><span style=\"font-weight: 400;\">A quadrilateral with one pair of parallel sides<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">A quadrilateral with no parallel sides<\/span><\/p><\/td><\/tr><tr><td><p><b>Trapezium<\/b><\/p><\/td><td><p><span style=\"font-weight: 400;\">A quadrilateral with no parallel sides<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">A quadrilateral with one pair of parallel sides<\/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-4295317\" data-id=\"4295317\" 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-16830e6 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"16830e6\" 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-2ec07d1\" data-id=\"2ec07d1\" 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-43cf960\" data-id=\"43cf960\" 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-7daf1f5 elementor-widget elementor-widget-heading\" data-id=\"7daf1f5\" 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\">Trapezoid Properties<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3410466 elementor-widget elementor-widget-text-editor\" data-id=\"3410466\" 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;\">These are the key trapezoid properties you should remember:<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>It has four sides and four angles.<\/b><span style=\"font-weight: 400;\"> It is a type of quadrilateral.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>At least one pair of sides is parallel.<\/b><span style=\"font-weight: 400;\"> These are the bases.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>The angles add up to 360\u00b0.<\/b><span style=\"font-weight: 400;\"> This is true for every quadrilateral.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Angles on the same leg add up to 180\u00b0.<\/b><span style=\"font-weight: 400;\"> For example, the two angles touching one leg are supplementary.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>It has two diagonals.<\/b><span style=\"font-weight: 400;\"> The diagonals cross each other inside the shape, but they usually do not cut each other in half.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>The median is parallel to the bases.<\/b><span style=\"font-weight: 400;\"> Its length is the average of the two bases: (a + b) \u00f7 2.<\/span><\/li><\/ol><h3><b>Types of Trapezoids<\/b><\/h3><p><span style=\"font-weight: 400;\">There are three main types:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Scalene trapezoid:<\/b><span style=\"font-weight: 400;\"> All four sides have different lengths, and no angles are equal.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Isosceles trapezoid:<\/b><span style=\"font-weight: 400;\"> The two legs are equal in length.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Right trapezoid:<\/b><span style=\"font-weight: 400;\"> It has two right angles (90\u00b0) next to one leg.<\/span><\/li><\/ul><h2><b>Isosceles Trapezoid: Special Properties<\/b><\/h2><p><span style=\"font-weight: 400;\">An isosceles trapezoid is the most popular type in exams. Its two legs are the same length, and it looks balanced, like a mirror image.<\/span><\/p><p><span style=\"font-weight: 400;\">Here are the special properties of an isosceles trapezoid:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>The legs are equal.<\/b><span style=\"font-weight: 400;\"> Both slanted sides have the same length.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>The base angles are equal.<\/b><span style=\"font-weight: 400;\"> The two angles on the longer base are the same. The two angles on the shorter base are also the same.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>The diagonals are equal.<\/b><span style=\"font-weight: 400;\"> Both diagonals have the same length.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Opposite angles add up to 180\u00b0.<\/b><span style=\"font-weight: 400;\"> This means an isosceles trapezoid can fit inside a circle.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>It has one line of symmetry.<\/b><span style=\"font-weight: 400;\"> The line goes through the midpoints of both bases.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">If you fold an isosceles trapezoid along its line of symmetry, the two halves match exactly.<\/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-6bb050a\" data-id=\"6bb050a\" 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-cf562e8 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"cf562e8\" 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-3a56db9\" data-id=\"3a56db9\" 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-b1464be\" data-id=\"b1464be\" 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-4a103fc elementor-widget elementor-widget-heading\" data-id=\"4a103fc\" 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 Trapezoid: Formula and Meaning<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-91c5819 elementor-widget elementor-widget-text-editor\" data-id=\"91c5819\" 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 trapezoid tells you how much flat space is inside the shape. It is measured in square units, such as cm\u00b2, m\u00b2, or square feet.<\/span><\/p><h3><b>Area of Trapezoid Formula<\/b><\/h3><p><span style=\"font-weight: 400;\">The <\/span><b>trapezoid area formula<\/b><span style=\"font-weight: 400;\"> is:<\/span><\/p><p><b>Area = \u00bd \u00d7 (a + b) \u00d7 h<\/b><\/p><p><span style=\"font-weight: 400;\">Here:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>a<\/b><span style=\"font-weight: 400;\"> = length of the first base<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>b<\/b><span style=\"font-weight: 400;\"> = length of the second base<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>h<\/b><span style=\"font-weight: 400;\"> = height (the straight distance between the bases)<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">In simple words: add the two parallel sides, multiply by the height, then divide by 2.<\/span><\/p><h3><b>Why Does the Area of Trapezoid Formula Work?<\/b><\/h3><p><span style=\"font-weight: 400;\">Imagine you make a copy of your trapezoid and flip it upside down. Now place the copy next to the original. Together, they form a <\/span><b>parallelogram<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><span style=\"font-weight: 400;\">The base of this parallelogram is (a + b), and its height is h. So its area is (a + b) \u00d7 h.<\/span><\/p><p><span style=\"font-weight: 400;\">But you used two trapezoids to make it. So one trapezoid is half of that: <\/span><b>\u00bd \u00d7 (a + b) \u00d7 h<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h3><b>How to Find the Area of a Trapezoid: Step by Step<\/b><\/h3><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find the two parallel sides (bases) and write down their lengths.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find the height. Make sure it is the straight distance, not the slanted leg.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Add the two bases together.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply the sum by the height.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Divide the answer 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><h2><b>Solved Examples<\/b><\/h2><h3><b>Example 1: Basic Area of Trapezoid<\/b><\/h3><p><span style=\"font-weight: 400;\">A trapezoid has bases of 8 cm and 12 cm. Its height is 5 cm. Find the area.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area = \u00bd \u00d7 (a + b) \u00d7 h<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area = \u00bd \u00d7 (8 + 12) \u00d7 5<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area = \u00bd \u00d7 20 \u00d7 5<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area = \u00bd \u00d7 100<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Area = 50 cm\u00b2<\/b><\/li><\/ul><h3><b>Example 2: Area of an Isosceles Trapezoid<\/b><\/h3><p><span style=\"font-weight: 400;\">An isosceles trapezoid has bases of 14 m and 6 m. Each leg is 5 m long. The height is not given, so we must find it first.<\/span><\/p><p><b>Step 1: Find the extra length on each side.<\/b><span style=\"font-weight: 400;\"> The longer base is 14 m and the shorter base is 6 m. The difference is 14 \u2212 6 = 8 m. Because the shape is symmetrical, each side has 8 \u00f7 2 = 4 m of extra length.<\/span><\/p><p><b>Step 2: Find the height.<\/b><span style=\"font-weight: 400;\"> The leg, the extra length, and the height make a right triangle. Use the Pythagoras theorem:<\/span><\/p><p><span style=\"font-weight: 400;\">h\u00b2 = 5\u00b2 \u2212 4\u00b2 = 25 \u2212 16 = 9<\/span><\/p><p><span style=\"font-weight: 400;\">So, h = 3 m.<\/span><\/p><p><b>Step 3: Find the area.<\/b><span style=\"font-weight: 400;\"> Area = \u00bd \u00d7 (14 + 6) \u00d7 3 = \u00bd \u00d7 20 \u00d7 3 = <\/span><b>30 m\u00b2<\/b><\/p><h3><b>Example 3: Find a Missing Base<\/b><\/h3><p><span style=\"font-weight: 400;\">The area of a trapezoid is 60 cm\u00b2. One base is 7 cm and the height is 6 cm. Find the other base.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">60 = \u00bd \u00d7 (7 + b) \u00d7 6<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">60 = 3 \u00d7 (7 + b)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">20 = 7 + b<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>b = 13 cm<\/b><\/li><\/ul><h2><b>Perimeter of a Trapezoid<\/b><\/h2><p><span style=\"font-weight: 400;\">The perimeter is the total distance around the shape. Just add all four sides:<\/span><\/p><p><b>Perimeter = a + b + c + d<\/b><\/p><p><span style=\"font-weight: 400;\">For an isosceles trapezoid, the legs are equal, so the formula becomes: <\/span><b>Perimeter = a + b + 2c<\/b><span style=\"font-weight: 400;\">, where c is the length of one leg.<\/span><\/p><h2><b>Volume of Trapezoid: Is It Possible?<\/b><\/h2><p><span style=\"font-weight: 400;\">This is a question many people search for, so let us answer it clearly.<\/span><\/p><p><span style=\"font-weight: 400;\">A trapezoid is a <\/span><b>flat, two-dimensional (2D) shape<\/b><span style=\"font-weight: 400;\">. It has length and width, but no depth. Because of this, a trapezoid <\/span><b>does not have a volume<\/b><span style=\"font-weight: 400;\">. Only 3D solids have volume.<\/span><\/p><p><span style=\"font-weight: 400;\">However, when people ask about the &#8220;volume of trapezoid,&#8221; they usually mean a <\/span><b>trapezoidal prism<\/b><span style=\"font-weight: 400;\">. This is a 3D solid whose two ends are trapezoids. Think of a ramp, a water channel, or a tent.<\/span><\/p><h3><b>Volume of a Trapezoidal Prism<\/b><\/h3><p><b>Volume = Area of the trapezoid \u00d7 Length of the prism<\/b><\/p><p><span style=\"font-weight: 400;\">Or, in full:<\/span><\/p><p><b>Volume = \u00bd \u00d7 (a + b) \u00d7 h \u00d7 L<\/b><\/p><p><span style=\"font-weight: 400;\">Here, L is the length (the distance between the two trapezoid ends).<\/span><\/p><p><b>Example:<\/b><span style=\"font-weight: 400;\"> A trapezoidal prism has trapezoid bases of 6 cm and 10 cm, and a trapezoid height of 4 cm. The prism is 12 cm long.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Area of the trapezoid = \u00bd \u00d7 (6 + 10) \u00d7 4 = 32 cm\u00b2<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Volume = 32 \u00d7 12<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Volume = 384 cm\u00b3<\/b><\/li><\/ul><p><span style=\"font-weight: 400;\">Notice that volume is in <\/span><b>cubic units<\/b><span style=\"font-weight: 400;\"> (cm\u00b3), while area is in <\/span><b>square units<\/b><span style=\"font-weight: 400;\"> (cm\u00b2).<\/span><\/p><p>Read More: <strong><a href=\"https:\/\/oratrics.com\/blogs\/english-concept\/how-to-pronounce-words\/\">How to Pronounce Words Like Entrepreneur<\/a><\/strong><\/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-4391241\" data-id=\"4391241\" 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-b7945dd elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"b7945dd\" 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-19e8582\" data-id=\"19e8582\" 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-3a98e99\" data-id=\"3a98e99\" 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-0ef0c38 elementor-widget elementor-widget-heading\" data-id=\"0ef0c38\" 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\">Quick Summary Table<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0556785 elementor-widget elementor-widget-text-editor\" data-id=\"0556785\" 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>Topic<\/b><\/p><\/td><td><p><b>Key Fact<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Trapezoid definition<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">A quadrilateral with one pair of parallel sides (US meaning)<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Area formula<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">\u00bd \u00d7 (a + b) \u00d7 h<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Perimeter<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">a + b + c + d<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Angle sum<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">360\u00b0<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Isosceles trapezoid<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Equal legs, equal base angles, equal diagonals<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Volume<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Not applicable to a 2D shape; use a trapezoidal prism: \u00bd \u00d7 (a + b) \u00d7 h \u00d7 L<\/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-313ce0e\" data-id=\"313ce0e\" 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-2e2de12 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"2e2de12\" 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-292e1d0\" data-id=\"292e1d0\" 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-51da221\" data-id=\"51da221\" 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-9f48781 elementor-widget elementor-widget-heading\" data-id=\"9f48781\" 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-46b86bc elementor-widget elementor-widget-accordion\" data-id=\"46b86bc\" 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-7411\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-7411\" 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 a trapezoid in simple words?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7411\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-7411\"><p><span style=\"font-weight: 400;\">A trapezoid is a four-sided flat shape that has one pair of parallel sides.<\/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-7412\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-7412\" 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 area of trapezoid formula?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7412\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-7412\"><p><span style=\"font-weight: 400;\">The formula is Area = \u00bd \u00d7 (a + b) \u00d7 h, where a and b are the parallel sides and h is the height.<\/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-7413\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-7413\" 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 a trapezoid have a volume?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7413\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-7413\"><p><span style=\"font-weight: 400;\">No, a trapezoid is a flat 2D shape, so it has no volume. A trapezoidal prism, which is a 3D shape, does have a volume.<\/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 a trapezoid in simple words?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">A trapezoid is a four-sided flat shape that has one pair of parallel sides.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"What is the area of trapezoid formula?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">The formula is Area = \\u00bd \\u00d7 (a + b) \\u00d7 h, where a and b are the parallel sides and h is the height.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Can a trapezoid have a volume?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">No, a trapezoid is a flat 2D shape, so it has no volume. A trapezoidal prism, which is a 3D shape, does have a volume.<\\\/span><\\\/p>\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\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-76cb74d\" data-id=\"76cb74d\" 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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Trapezoid: Shape, Properties, Area Formula and Easy Examples A trapezoid is a flat shape with four straight sides. In the [&hellip;]<\/p>\n","protected":false},"author":10,"featured_media":31415,"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-31412","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 v28.8 - 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