Question

The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 655 cm², find the length of the parallel sides.

Answer 1

The ratio of parallel sides of the trapezium = 10: 13.
Distance between them = 25 cm
Area of trapezium = 655 cm²
Let the common ratio be 𝑥,
Then, the parallel sides are 10x, 13x
Area of trapezium formula is $\frac{1}{2}$(a + b) h
Area of trapezium = 655 cm²
$\frac{1}{2}$ (10 𝑥 + 13 𝑥) 25 = 655
23 𝑥 $\times$ 25 = 655 $\times$ 2
575 𝑥 = 1310
𝑥 = 2.278
the parallel sides of the trapezium are 10 x 2.278 = 22.78, 13 x 2.278 = 29.617
Therefore, the length of parallel sides of a trapezium are 22.78 cm, 29.617 cm.