How to find the area of a Trapezium?

The trapezium, which is also known as the trapezoid, is a closed quadrilateral that contains a pair of parallel sides.
Area of a trapezium is the number of unit squares that can fit into the trapezium, and it is measured in square units.

Area of Trapezium Formula

The area of any closed figure is the space enclosed within this object. The area of a trapezium or trapezoid is obtained using parallel lines and the distance between them. In the case of trapezium, the area is given by, 

 Area = 1/2 × (Sum of parallel sides) × (Distance between them)

Let's assume the a and b to be the parallel sides of the trapezium and h to be the distance between them. Let the area of the trapezium be denoted by A. We have, 

A = 1/2 × (a + b) × h square units

Solved Examples on the Area of Trapezium

Example 1: Find the area of the trapezium with the sum of the parallel sides being 40 m and the height being 20 m.

Solution: 

Sum of the parallel sides = 40 m

Height of the trapezium = 20 m

As we know that, Area of trapezium = 1/2 × (Sum of the parallel sides) × Height

Area of trapezium = 1/2 × (40) × 20

Area of trapezium = 400 m²

Example 2: If the sum of the parallel sides of the trapezium is double the height and the area of the trapezium is 400 m². Then find the sum of the parallel sides of the trapezium and its height.

Solution:

Given, Sum of the parallel sides of the trapezium is double its height

Height of the trapezium = 8 cm,

then, Sum of the parallel sides of the trapezium = 2 × 8 = 16 cm

As we know that, Area of trapezium = 1/2 × (Sum of the parallel sides) × Height

Area = 1/2 × 16 × 8

Area = 64 cm²

Related Resources

• Area of Parallelogram
• Area of Triangles
• Area of Square