# How to Find the Area of a Trapezoid

## Finding the Area of a Trapezoid

The area of a trapezoid is found using the formula:

In this formula, **b _{1}** and

**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:

## Interactive Widget

Use this **interactive widget** to create a trapezoid and then calculate its area. Start by clicking in the shaded area.

**Oops, it's broken!Turn your phone on its side to use this widget.**

## 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}.