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*r2. By substitution: max. area of inscribed semicircle = pi*[s2*(3 - 2*SQRT(2))]
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