side of the large square
‘s’ = side of the small square
‘r’ = radius of the circle and semicircle.
The area of the large square inscribed in the circle:
(S/2)2 + (S/2)2 = r2
Hence, the area of the large square is: S2 =
The area of the small square inscribed in the semicircle:
(s/2)2 + s2 = r2
Hence, the area of the small square:
s^2 = (4/5)r2
Thus: s2 / S2 = 2/5
also the interesting visual proof below:
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