# SOLUTION: A semicircle is placed on one side of a square so that its diameter coincides with a side of the square. Find the side length of the square if the total area of the square plus the

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 Click here to see ALL problems on Geometry Word Problems Question 58255: A semicircle is placed on one side of a square so that its diameter coincides with a side of the square. Find the side length of the square if the total area of the square plus the semicircle is 200 square inches.Answer by ankor@dixie-net.com(15747)   (Show Source): You can put this solution on YOUR website! A semicircle is placed on one side of a square so that it's diameter coincides with a side of the square. Find the side length of the square if the total area of the square plus the semicircle is 200 square inches. : Let x = one side & diamter of the semicircle : Square area + semicircle area = 200 Radius = .5x x^2 + (pi(.5x)^2)/2 = 200 x^2 + (pi*.25x^2)/2 = 200 2x^2 + pi*.25x^2 = 400; multiplied eq by 2 2x^2 + .785x^2 = 400 2.785x^2 = 400 x^2 = 400/2.785 x^2 = 143.6 x = SqRt[143.6] x = 11.98 ~ 12 inches: Check: r = 6 inches; 144 + (pi*36)/2 = 200.55 ~ 200