▸▸▸

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?

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!

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.