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avatar+464 

this Question is different from the other because it has angles.

 Oct 14, 2018
 #1
avatar+98130 
+1

We can use symmetry to solve this

 

The area  of  the 60 degree sector on the right is given by  pi *12^2 * 1/6  = 144/6 pi =

 

24 pi  units^2

 

The area  of the  triangle on the right =  (1/2)(12^2)sqrt (3)/ 2 =  36sqrt3  units^2

 

So...half of the shaded area =  the differences in these areas

 

So....the whole shaded area  = twice this  =

 

2 [ 24 pi - 36sqrt 3 ]  =  [48pi - 72sqrt3 units^2] ≈  26.09 units^2

 

 

cool cool cool 

 Oct 14, 2018
 #2
avatar+464 
+1

Thank you so much once again Chris 

 Oct 14, 2018

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