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Question

# The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10 cm and its altitude is 8 cm. Its area is

A
128cm2
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B
112cm2
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C
118cm2
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D
124cm2
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Solution

## The correct option is A 128cm2As shown in figure, ADE is a triangle. ∴DE2=102−82=62or DE=6cmBy symmetry, FC=6 cmLet AB =xThen (x+10+6+x+6+10)=52or 2x+32=52 or x=10 cm ∴ Area of trapeziumApplying the formula for area of trapezium 12×(AB+DC)×BF where AB and DC are parallel sides and BF is distance between them=12(10+22)×8=128cm2

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