##### Related Pages

# Area of a Trapezoid

(KS3, Year 7)

## The Lesson

The area of a trapezoid is found using the formula:In this formula,

**b**and

_{1}**b**are the lengths of the bases of the trapezoid and

_{2}**h**is the height of the trapezoid. The image below shows what we mean by the lengths of the bases and the height:

## 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(b

_{1}+ b_{2})h**Don't forget:**½(b_{1}+ b_{2})h = ½ × (b_{1}+ b_{2}) × h# 2

Substitute the length of the bases and the height into the formula. In our example, b

_{1}= 3, b_{2}= 5 and h = 3.
Area = ½ × (3 + 5) × 2
Area = ½ × (8) × 2
Area = 8 cm

^{2}**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 cm^{2}.

## "Find the Area" Widget

## 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.## A Note on Units

The area of a trapezoid is a length times a length, so we say its dimension is length^{2}. (All areas are lengths squared). This affects the units used. If the lengths of a rectangle are in cm, the area is in cm

^{2}. If the lengths are in inches, the area is in inches

^{2}.

**Help Us To Improve Mathematics Monster**

- Do you disagree with something on this page?
- Did you spot a typo?