# How to find the area of a trapezium with examples

The area of a trapezium is one-half of the product of the sum of its parallel sides and height. A trapezium is a four-sided plane figure which has one pair of opposite sides parallel but not equal. On this page, we will discuss the area of a trapezium in detail.

## What is the area of a trapezoid?

The area of a trapezium is half of the product of the sum of its parallel sides and height. Only a pair of opposite sides of a trapezium is parallel but they are not equal. In finding the area of a trapezoid we take half of the product of the sum of its parallel sides and the height.

\text{Therefore, the formula for finding the area of a trapezium is} = \frac{1}{2}× (\text{sum of its parallel sides) × height}\\
= \frac{1}{2}×(a + b)×h

## How to find the area of a trapezium

In finding the area of a trapezoid, follow the steps below:

• make sure all measurements of the lengths of the side of the trapezium are of the same units.

• The height must be at a right angle to the parallel sides. Note: the common mistake students do is the take the slanted height as the height of the trapezium, this should not be the case.

• sum the parallel sides and multiply it by the height and take half of the product eg. 1/2 × (a+b)×h

• Simplify to get the area of the trapezium.

Let’s understand more by working through some examples.

Example 1: The parallel sides of a trapezium are 22cm and 14cm long. The distance between the parallel sides is 10cm. what is the area of the trapezium?

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solution

From the question given, the length of the parallel sides of a trapezium is a = 22cm and b = 14cm. The distance between the parallel sides of the trapezium is the height of the trapezium, h=10cm.

\text{The area of a trapezium is}\\\begin{aligned} &=\frac{1}{2}×(a + b) × h\\
&= \frac{1}{2} × (22 + 14) × 10\\
&=\frac{1}{2}×(36)×10\\
&= 18×10,\space\text {since} \frac{1}{2}×36=18\\
&=180cm^2\\\end{aligned}

This is pretty cool, right?

Example 2: Find the area of the trapezium below

Solution

The length of the parallel sides of the trapezium is a = 8cm and b = 4cm. The height of the trapezium (h)= 5cm.

\text{The Area of a trapezium is} \space\\ \begin{aligned}&= \frac{1}{2}× (\text{sum of parallel sides}) × \text{height}\\
&= \frac{1}{2}×(a + b)×h\\
&= \frac{1}{2}×(8+4)×5\\
&= \frac{1}{2}×(12)×5\\
&= 6×5, \text{since }\space \frac{1}{2}×12 =6\\
&= 30cm^2\end{aligned}