Question

# Find the area of shaded region, if in parallelogram ABCD, ∠PBQ=∠SDR = 60o, BP=BQ=SD=RD= 21 cm, BC = 45 cm and MN = 20 cm.

A
231 cm2
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B
438 cm2
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C
669 cm2
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D
897 cm2
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Solution

## The correct option is B 438 cm2As BP=BQ= radius, PQ is part of circle, region sector is sector with ∠PBQ is 60o Similarly As SD=RD= radius, SR is part of circle, region SDR is sector with ∠SDR is 60o Area of shaded region = area of parallelogram ABCD - area of sector PBQ - area of sector SDR ​ Area of parallelogram = base×height = BC×MN = 45×20 = 900 cm2 Area of sector PBQ = angle360o×πr2 = 60o360o×227×212 = 16×227×441 = 11×21 = 231 cm2 As sector PBQ and SDR has same angle and radius, these two sector will have same area. ⟹Area of sector SDR = Area of sector PBQ = 231 cm2 Area of shaded region = 900 - 231 - 231 = 438 cm2

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