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The perimeter of a trapezium is 52 cm. Its non-parallel sides are 10 cm each and the distance between two parallel sides is 8 cm. Find the area of the trapezium.

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128 sq cm

129 sq cm

130 sq cm

135 sq cm

answer is A.

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Detailed Solution

It is given that the perimeter of a trapezium is 52 cm and the distance between the two parallel sides that mean the height of the trapezium is 8 cm and the distance between the non-parallel sides is 10 cm.

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The perimeter of a trapezium

= 10 + x + y + 10

52 = 20 + x + y

x + y = 52 - 20

x + y = 32

The sum of the parallel sides of a given trapezium is 32 cm.
The area of the given trapezium =

A = 12 \times (Sum of parallel sides) \times h

Since

h = 8 cm

The area of the trapezium =

A = 12 \times (32) \times 8

The area of the trapezium =

A = 16 \times 8

The area of the trapezium =

A = 128

Hence, the area of the trapezium is

128 c m^{2}

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The perimeter of a trapezium is 52 cm. Its non-parallel sides are 10 cm each and the distance between two parallel sides is 8 cm. Find the area of the trapezium.

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