solid mensuration
posted by Cathy on .
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.

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