Question

The area of a trapezium with equal non-parallel sides is 168 m². If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.

Answer 1

Length of the parallel sides are 36 m and 20 m.

Area of a trapezium = 168 m²

∵ Area of a trapezium = `1/2 xx ["Sum af parallel sides"] xx "Height"`

∴ `168 = 1/2 xx [36 + 20] xx "Height"`

⇒ Height = `(168 xx 2)/56 = 336/56` = 6 m

In ΔACB, using Pythagoras theorem,

(AB)² = (BC)² + (AC)²

⇒ (AB)² = (8)² + (6)²

⇒ (AB)² = 64 + 36

⇒ (AB)² = 100

∴ AB = `sqrt(100)` = 10 m

Hence, length of the non-parallel side is 10 m.