Question

The difference between the lengths of the parallel sides of a trapezium is 8 cm, the perpendicular distance between these sides is 24 cm and the area of the trapezium is 312 cm². Find the length of each of the parallel sides.

Answer 1

Given:
Area = 312 cm²

$$\begin{gathered} a-b=8 \\ a=8+b \end{gathered}$$

Height = 24 cm
Area of trapezium = $\frac{1}{2}\left(\mathrm{Sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\right)\times \mathrm{Height}$
$$\begin{gathered} \Rightarrow 312=\frac{1}{2}\times \left(8+b+b\right)\times 24 \\ \Rightarrow \frac{624}{24}=8+2b \\ \Rightarrow 26=8+2b \\ \Rightarrow 18=2b \\ \Rightarrow b=9\mathrm{cm} \end{gathered}$$

$$\begin{gathered} a=8+b \\ a=8+9 \\ a=17\mathrm{cm} \end{gathered}$$

Thus, the lengths of parallel sides are 17 cm and 9 cm.