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Four enclosed arcs produced with the same radius are inscribed in such a way, as shown in the image below.

What percentage of area is the green area, compared to the square, when s = 10?

 

 Jul 12, 2020
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s divided by the square root of 2 will give you the radius of the circle.

 

s / sqrt(2)  =  10 / sqrt(2)  =  5·sqrt(2)

 

The area of the (full) circle will be:  pi · [ 5·sqrt(2) ]2  =  50·pi

 

The area of the square = 100   

     --->   the area of the green portion  =  [ ( 50·pi ) - ( 100 ) ] / 2  =  25·pi - 50

 Jul 12, 2020

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