The semicircle of radius r will will be tangent to two sides of the square of side s.
s will equal r + r/SQRT(2), thus
r will equal s*(2  SQRT(2)).
The maximum area of a semicircle = (1/2) * pi*r^{2}.
By substitution:
max. area of inscribed semicircle
= pi*[s^{2}*(3  2*SQRT(2))]

Posted by Dej Mar
on 20121228 18:49:44 