A copy of a trapezium, rotated 180°, and joined with the original creates a parallelogram, so a trapezium can be thought of as half a parallelogram.

The area of a trapezium, therefore, can be thought of as the area of the parallelogram, divided by 2.

So area (A) is half of the top (a) + the base (b), multiplied by the height (h), calculated using this formula:

𝑨 = 1/2 (𝒂 + 𝒃)𝒉.

For example, this trapezium is 2.5 cm along the top (a), 5 cm along the base (b) and 3 cm in height (h).

So the area is:

1/2 (2.5 + 5)3

Breaking this down: the part in brackets is always calculated first. The number after the brackets is then multiplied by this.

So the area is:

(𝒂 + 𝒃) = 2.5 + 5 = 7.5
multiplied by 𝒉 = 7.5 x 3 = 22.5
22.5 ÷ 2 = 11.25 cm²

Try it out

What is the area of this trapezium, which measures 3 cm along the top (a) 4 cm along the base (b) and 2 cm in height (h)?

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