Area of a trapezium

The area of a trapezium is given by {A}=\frac{(a+b)}{2}\times{h}.

Trapezium diagramDiagram of two identical trapezia (or trapeziums)

You can see that this is true by taking two identical trapezia (or trapeziums) to make a parallelogram.

Diagram of two identical trapezia, with one trapezium turned through 180°

Area of a trapezium

Turn one trapezium through 180°.

For a parallelogram, the area is {A}={b}\times{h}

So, area of {2} trapeziums = {(a + b)} \times {h}

Area of {1} trapezium = \frac{1}{2} \times {(a + b)} \times {h}

This becomes, for a trapezium, {A}=\frac{(a+b)}{2}\times{h}

curriculum-key-fact
Use the perpendicular height of the trapezium, not the sloping height.
Question

Find the area of this trapezium:

Diagram of a paralelogram showing values for base (a + b) and height (h)

The area is {A}=\frac{(4+10)}{2}\times{6}

={42~cm}^{2}

Remember to use the perpendicular height of the trapezium.

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