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Question

From the adjacent diagram, find the area of the shaded region.

  1. fraction numerator square root of 3 over denominator 2 end fraction left parenthesis 2 minus pi right parenthesis c m to the power of 2 end exponent    
  2. fraction numerator 9 over denominator 2 end fraction left parenthesis 2 square root of 3 minus pi right parenthesis c m to the power of 2 end exponent    
  3. fraction numerator 9 over denominator 2 end fraction left parenthesis 2 square root of 3 plus pi right parenthesis c m to the power of 2 end exponent    
  4. fraction numerator 3 over denominator 2 end fraction open parentheses square root of 3 minus pi close parentheses c m to the power of 2 end exponent    

The correct answer is: fraction numerator 9 over denominator 2 end fraction left parenthesis 2 square root of 3 minus pi right parenthesis c m to the power of 2 end exponent


    A r e a space o f space s h a d e d space r e g i o n space equals A r e a space o f space e q u i l a t e r a l space t r i a n g l e space o f space s i d e space 6 space c m space minus 3 A r e a space o f space t h e space a r c space w i t h space r a d i u s space 3 space c m
A r e a space o f space e q u i l a t e r a l space t r i a n g l e space equals fraction numerator square root of 3 over denominator 4 end fraction a squared
A r e a space o f space a r c space w i t h space a n g l e space theta equals theta over 360 πR squared
Area space of space shaded space region equals fraction numerator square root of 3 over denominator 4 end fraction cross times 6 cross times 6 minus 60 over 360 cross times straight pi cross times 3 cross times 3
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator square root of 3 over denominator 2 end fraction 36 minus straight pi over 2 3
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 over 2 left parenthesis 6 square root of 3 minus straight pi right parenthesis

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