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Two sectors of a circle of radius $12$ overlap as shown, with $P$ and $R$ as the centers of the respective circles. Determine the area of the shaded region.

 

 

 Jun 29, 2018
 #1
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We can find half of the area of the shaded region as follows

 

Area of a sector of 1/6 of a circle with a radius of 12  - Area of a triangle with sides of 12 and an included angle of 60°   =

 

(1/2) 12^2 ( pi/3)  - (1/2) 12^2 sin (60)  =

 

(1/2) 12^2  (  pi /3  - √3/2)

 

So...the  shaded area  is twice this  =

 

12^2 ( pi /3  - √3/2) units^2  ≈  26.1  units^2

 

 

cool cool cool

 Jun 29, 2018
 #2
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unfortunately your answer was incorrect; do you think it would be correct if I type in your non-approximated answer? 

Guest Jun 29, 2018

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