*‘S’ =
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} = r^{2}

Hence, the area of the large square is: S^{2} =
2r^{2}

The area of the small square inscribed in the semicircle:

(s/2)^{2} + s^{2} = r^{2}

Hence, the area of the small square:

s^2 = (4/5)r^{2}

Thus: s^{2} / S^{2} = **2/5**

*See
also the interesting visual proof below:*

Please spread the word about the Sunday Puzzle!