Trapezoid: Shape, Properties, Area Formula and Easy Examples

A trapezoid is a flat shape with four straight sides. In the most common school definition, it has one pair of parallel sides. Parallel sides are sides that never meet, no matter how far you extend them.

The two parallel sides are called the bases. The other two sides are called the legs. The distance between the two bases is called the height. 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.

So, if someone asks, “what is trapezoid in maths?”, here is a short answer: it is a four-sided shape (a quadrilateral) with at least one pair of parallel sides.

☰ Table of Contents

Trapezoid Shape: Main Parts

Before you learn any formula, it helps to know the parts of the trapezoid shape.

Base 1 (a): The top parallel side.
Base 2 (b): The bottom parallel side.
Legs (c and d): The two slanted sides.
Height (h): The straight, vertical distance between the two bases. It makes a right angle (90°) with both bases.
Median (m): A line that joins the midpoints of the two legs. It is parallel to the bases.

Difference Between Trapezium and Trapezoid

Many students get confused here, and it is a very common question. The difference between trapezium and trapezoid depends on which country’s English you use.

Term	In the US and Canada	In the UK, India, Australia and most other countries
Trapezoid	A quadrilateral with one pair of parallel sides	A quadrilateral with no parallel sides
Trapezium	A quadrilateral with no parallel sides	A quadrilateral with one pair of parallel sides

Trapezoid Properties

These are the key trapezoid properties you should remember:

It has four sides and four angles. It is a type of quadrilateral.
At least one pair of sides is parallel. These are the bases.
The angles add up to 360°. This is true for every quadrilateral.
Angles on the same leg add up to 180°. For example, the two angles touching one leg are supplementary.
It has two diagonals. The diagonals cross each other inside the shape, but they usually do not cut each other in half.
The median is parallel to the bases. Its length is the average of the two bases: (a + b) ÷ 2.

Types of Trapezoids

There are three main types:

Scalene trapezoid: All four sides have different lengths, and no angles are equal.
Isosceles trapezoid: The two legs are equal in length.
Right trapezoid: It has two right angles (90°) next to one leg.

Isosceles Trapezoid: Special Properties

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.

Here are the special properties of an isosceles trapezoid:

The legs are equal. Both slanted sides have the same length.
The base angles are equal. The two angles on the longer base are the same. The two angles on the shorter base are also the same.
The diagonals are equal. Both diagonals have the same length.
Opposite angles add up to 180°. This means an isosceles trapezoid can fit inside a circle.
It has one line of symmetry. The line goes through the midpoints of both bases.

If you fold an isosceles trapezoid along its line of symmetry, the two halves match exactly.

Area of Trapezoid: Formula and Meaning

The area of a trapezoid tells you how much flat space is inside the shape. It is measured in square units, such as cm², m², or square feet.

Area of Trapezoid Formula

The trapezoid area formula is:

Area = ½ × (a + b) × h

Here:

a = length of the first base
b = length of the second base
h = height (the straight distance between the bases)

In simple words: add the two parallel sides, multiply by the height, then divide by 2.

Why Does the Area of Trapezoid Formula Work?

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 parallelogram.

The base of this parallelogram is (a + b), and its height is h. So its area is (a + b) × h.

But you used two trapezoids to make it. So one trapezoid is half of that: ½ × (a + b) × h.

How to Find the Area of a Trapezoid: Step by Step

Find the two parallel sides (bases) and write down their lengths.
Find the height. Make sure it is the straight distance, not the slanted leg.
Add the two bases together.
Multiply the sum by the height.
Divide the answer by 2.
Write the answer in square units.

Solved Examples

Example 1: Basic Area of Trapezoid

A trapezoid has bases of 8 cm and 12 cm. Its height is 5 cm. Find the area.

Area = ½ × (a + b) × h
Area = ½ × (8 + 12) × 5
Area = ½ × 20 × 5
Area = ½ × 100
Area = 50 cm²

Example 2: Area of an Isosceles Trapezoid

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.

Step 1: Find the extra length on each side. The longer base is 14 m and the shorter base is 6 m. The difference is 14 − 6 = 8 m. Because the shape is symmetrical, each side has 8 ÷ 2 = 4 m of extra length.

Step 2: Find the height. The leg, the extra length, and the height make a right triangle. Use the Pythagoras theorem:

h² = 5² − 4² = 25 − 16 = 9

So, h = 3 m.

Step 3: Find the area. Area = ½ × (14 + 6) × 3 = ½ × 20 × 3 = 30 m²

Example 3: Find a Missing Base

The area of a trapezoid is 60 cm². One base is 7 cm and the height is 6 cm. Find the other base.

60 = ½ × (7 + b) × 6
60 = 3 × (7 + b)
20 = 7 + b
b = 13 cm

Perimeter of a Trapezoid

The perimeter is the total distance around the shape. Just add all four sides:

Perimeter = a + b + c + d

For an isosceles trapezoid, the legs are equal, so the formula becomes: Perimeter = a + b + 2c, where c is the length of one leg.

Volume of Trapezoid: Is It Possible?

This is a question many people search for, so let us answer it clearly.

A trapezoid is a flat, two-dimensional (2D) shape. It has length and width, but no depth. Because of this, a trapezoid does not have a volume. Only 3D solids have volume.

However, when people ask about the “volume of trapezoid,” they usually mean a trapezoidal prism. This is a 3D solid whose two ends are trapezoids. Think of a ramp, a water channel, or a tent.

Volume of a Trapezoidal Prism

Volume = Area of the trapezoid × Length of the prism

Or, in full:

Volume = ½ × (a + b) × h × L

Here, L is the length (the distance between the two trapezoid ends).

Example: 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.

Area of the trapezoid = ½ × (6 + 10) × 4 = 32 cm²
Volume = 32 × 12
Volume = 384 cm³

Notice that volume is in cubic units (cm³), while area is in square units (cm²).

Quick Summary Table

Topic	Key Fact
Trapezoid definition	A quadrilateral with one pair of parallel sides (US meaning)
Area formula	½ × (a + b) × h
Perimeter	a + b + c + d
Angle sum	360°
Isosceles trapezoid	Equal legs, equal base angles, equal diagonals
Volume	Not applicable to a 2D shape; use a trapezoidal prism: ½ × (a + b) × h × L

Frequently Asked Questions

What is a trapezoid in simple words?

A trapezoid is a four-sided flat shape that has one pair of parallel sides.

What is the area of trapezoid formula?

The formula is Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the height.

Can a trapezoid have a volume?

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.