By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied by the height (the same formula as the one given above).

Let the parallel sides of the trapezium be $a$ and $b$ , and height be $h$ .

Divide the trapezium into two triangles.

$$\text{Area of first triangle} = \frac{1}{2}ah$$

$$\text{Area of second triangle} = \frac{1}{2}bh$$

Adding both areas:

$$\text{Area} = \frac{1}{2}ah + \frac{1}{2}bh$$

Taking $\frac{1}{2}h$ common:

$$\text{Area} = \frac{1}{2}(a + b)h$$

Hence, the area of a trapezium is half the sum of the parallel sides multiplied by the height.