Area of a Trapezium

Area of a Trapezium

GCSE(F),

Fit 2 trapezia together, side by side, to make a parallelogram.

The area of a parallelogram is base x perpendicular height.

For this parallelogram, area = (a + b) x height.

The parallelogram is equal to two trapezia, therefore the area of one trapezium is

`A = frac(1)(2)(a + b)h`

Examples

1. What is the area of the trapezium, shown below?

Answer: 170 cm2

Area of a trapezium = `frac(1)(2)(a + b)h`

A = `frac(1)(2) xx (14 + 20) xx 10` = 170

2. The parallel sides of a trapezium are 18 and 22 cm long. The area of the trapezium is 400 cm2. What is the perpendicular height of the trapezium?

Answer: 2.2 cm

Area of a trapezium = `frac(1)(2)(a + b)h`

`44 = frac(1)(2)(18 + 22) xx h`

`44 = 20h`

h = 2.2