# Area of a trapezium

The area of a trapezium is given by .

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

Area of a trapezium

Turn one trapezium through 180°.

For a parallelogram, the area is

So, area of trapeziums

Area of trapezium

This becomes, for a trapezium,

Use the perpendicular height of the trapezium, not the sloping height.
Question

Find the area of this trapezium:

The area is

Remember to use the perpendicular height of the trapezium.

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