WTMaths logo
Area of a Trapezium

Area of a Trapezium

The area of a trapezium is `A = frac(1)(2)(a + b)h`.

You do not need to know this, but this is why it works:

Fit two trapezia together, side by side, to make a parallelogram. One of the parallelograms needs to be flipped.

Area of a trapezium

The area of a parallelogram is base x perpendicular height. For this parallelogram, `text(area) = (a + b) xx height`.

The parallelogram is equal to two trapezia, therefore the area of one trapezium is `A = frac(1)(2)(a + b)h`

Example 1

What is the area of the trapezium, shown below?

Work out the area of trapezium

Area of Trapezium = `frac(1)(2)`(a + b) x h
Substitute `A` `= frac(1)(2)(14 + 20) xx 10`
Divide both sides by 20 `A` `= 170`

Answer: 170 cm2

Example 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?

Area of Trapezium = `frac(1)(2)`(a + b) x h
Substitute `400` `= frac(1)(2)(18 + 22)h`
400 `= 20h`
Divide both sides by 20 20 `= h`

Answer: 2.2 cm