Area of a Trapezoid
(KS3, Year 7)
The area of a trapezoid is found using the formula:

trapezoid 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:

trapezoid bh

How to Find the Area of a Trapezoid

Finding the area of a trapezoid is easy.

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? trapezoid

Step-by-Step:

1

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

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.

Answer:

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

"Find the Area" Widget

Here is a widget to help you learn the formulas to find the areas of different shapes.
  • Click on the shape you're learning about.
  • Click on the pad to start.
  • Follow the instructions in the bottom-left corner.
  • On the last click, the formula, workings, and answer will appear in the yellow box.
  • Enjoy!
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Lesson Slides

The slider below shows another real example of how to find the area of a trapezoid.

I Say Trapezoid, You Say 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.

trapezoid explained

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.
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This page was written by Stephen Clarke.