The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.                                                                                                                                                [Page No. 142]

Let parallel sides be $a = 40 \,\mathrm{cm}$, $b = 20 \,\mathrm{cm}$, and equal non-parallel sides = $26 \,\mathrm{cm}$ each.

Height of trapezium:

Drop perpendicular from each end of the shorter parallel side.

Horizontal distance on each side = $\frac{40 - 20}{2} = 10$ cm

Using Pythagoras: $h^2 + 10^2 = 26^2$

$$h^2 = 676 - 100 = 576$$

$$h = 24 \text{ cm}$$

Area of trapezium = $\frac{1}{2} \times$ (sum of parallel sides) $\times$ height

$$= \frac{1}{2} \times (40 + 20) \times 24$$

$$= \frac{1}{2} \times 60 \times 24 = 720 \text{ cm}^2$$