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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.

 

 Apr 20, 2021
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Dividing the  shaded  area  in half  from  the bottom left  vertex of the figure  to  the point of intersection  we  have  this  area :

 

Area of a quarter  circle  with  a radius  of 12  - area of a  right triangle with legs of 12  = 

 

pi (12)^2 / 4   =  (1/2) (12)^2   =   (12)^2  ( pi/4  - 1/2)    

 

And  by symmetry  the total shaded area  =

 

2 (12^2) ( pi/4  - 1/2)  =   288  ( pi/4 - 1/2) units^2  ≈  82.19  units^2

 

 

cool cool cool

 Apr 20, 2021

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