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Question

# Find the area of the parallelogram in which AD=5 cm, DE=3 cm and AB=10 cm. [AE is the height of the parallelogram]

A

15 cm2

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B

50 cm2

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C

30 cm2

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D

40 cm2

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Solution

## The correct option is D 40 cm2 Since, AE is the height of the parallelogram, so, AE is perpendicular to CD. ⇒△ADE is a right angled triangle, right angled at E. Applying Pythagoras Theorem in △ADE: AD2=AE2+DE2 ⇒AE2=AD2−DE2=52−32=16 ⇒AE=4 cm Now, in parallelogram ABCD, AB=10 cm⇒CD=10 cm [Opposite sides are parallel and equal in a parallelogram] Area of parallelogram ABCD= Base × Height Base =CD=10 cm Height =AE=4 cm ⇒ Area =CD×AE=10×4=40 cm2

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