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

Let the length of the parallel sides be x and x − 8.
The height of the trapezium = 24 cm

Area of trapezium = $\frac{1}{2}\times \mathrm{sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\times \mathrm{height}$
⇒ 312 = $\frac{1}{2}\times \left(x+x-8\right)\times 24$
⇒ 312 = 12(2x − 8)
⇒ 2x − 8 = $\frac{312}{12}$
⇒ 2x − 8 = 26
⇒ 2x = 26 + 8
⇒ 2x = 34
⇒ x = 17 cm

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