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.

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?

 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

 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