Posted by Cathy on Saturday, December 1, 2012 at 7:07am.
Find the area of a portion of a semicircle of radius 15 m that is outside the area of an inscribed square if the base of the square lies on the diameter of the semicircle.
Please include solution. Thanks.

solid mensuration  Reiny, Saturday, December 1, 2012 at 9:38am
make a sketch, putting the complete figure on the xy grid
draw a line from the centre of the semicircle to the vertex of the square , calling that point P(x,y)
so the base of the square is 2x and its height is y
so clearly
y = 2x
also x^2 + y^2 = 15^2
x^2 + (2x)^2 = 225
5x^2 = 225
x^2 = 45
x = 3√5
y = 6√5
area of square = 2xy
= 2(3√5)(6√5) = 180
area of semicircle = (1/2)π(15)^2 = 225π/2
area between square and semicircle
= 225π/2  180 or appr 173.43
check my arithmetic