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Question

The area of a trapezium is 459 cm2. Its parallel sides are in the ratio 7: 10 and the perpendicular distance between them is 9 cm. Find the length of each of the parallel sides.

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Solution

Area of a trapezium = 459 cm2

The ratio of parallel sides of the trapezium = 7 : 10

The perpendicular distance between parallel sides = 9 cm

Let the common ratio be x,

Then, the parallel sides are 7x, 10x

The area of the trapezium formula is 12(a+b)h

Area of trapezium = 459 cm2

12(a+b)h=459

12(7x+10x)9=459

12(17x)9=459

153x=459×2

153x=918

x=6

The parallel sides of the trapezium are 7 × 6 = 42 cm, 10 × 6 = 60 cm.

Therefore, the length of each parallel side is 42 cm, 60 cm.

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