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 x-y 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

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