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?

Guest Jul 12, 2020

#1**0 **

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

geno3141 Jul 12, 2020