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How to Find the Area of a Trapezoid (Mathematics Lesson)

How to Find the Area of a Trapezoid

The area of a trapezoid is found using the formula:



In this formula, b1 and b2 are the lengths of the bases of the trapezoid and h is the height of the trapezoid. The image below shows what we mean by the lengths of the bases and the height:

A Real Example of How to Find the Area of a Trapezoid

An Example Question

What is the area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm, as shown below?

Step 1
Start with the formula:
Area = ½(b1 + b2)h
Don't forget: ½(b1 + b2)h = ½ × (b1 + b2) × h

Step 2
Substitute the length of the bases and the height into the formula. In our example, b1 = 3, b2 = 5 and h = 3.
Area = ½ × (3 + 5) × 2
Area = ½ × (8) × 2
Area = 8 cm2
Don't forget: Calculate what's in the brackets () first (using the order of operations). In our example, (3 + 5) = 8

or: ½ × a number = 0.5 × a number = a number ÷ 2.

The area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm is 8 cm2.

Another Real Example of How to Find the Area of a Trapezoid

The slider below shows another real example of how to find the area of a trapezoid:
Curriculum
Geometry Lessons
Interactive Widget
Here is an interactive widget to help you learn about finding the area of a trapezoid.
Interactive Test
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Here's a second test on finding the area of a trapezoid.
Here's a third test on finding the area of a trapezoid.
Note

Trapezoid, Trapezium

The shape is called a trapezoid in North America.

In English speaking countries outside North America, a trapezoid is called a trapezium.

What Is a Trapezoid?

A trapezoid is a four-sided flat shape with straight sides. It has a pair of opposite sides which are parallel.

A Note on Units

The area of a trapezoid is a length times a length, so we say its dimension is length2. (All areas are lengths squared.)

This affects the units used. If the lengths of a rectangle are in cm, the area is in cm2. If the lengths are in inches, the area is in inches2.