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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.
  1. 438 cm2
  2. 231 cm2
  3. 897 cm2
  4. 669 cm2


Solution

The correct option is A 438 cm2
As 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×227×21216×227×441 = 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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