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?

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}

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