SOLUTION: The radius of a semi circle is 5 cm.A square is fitted inside the semi circle .Calculate the area of the square

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Question 1029427: The radius of a semi circle is 5 cm.A square is fitted inside the semi circle .Calculate the area of the square
Found 2 solutions by Fombitz, Boreal:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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From the diagram,
S%5E2%2B%282S%29%5E2=R%5E2
S%5E2%2B4S%5E2=R%5E2
5S%5E2=R%5E2
S%5E2=R%5E2%2F5
The area of a square with side, 2S, would be,
A=%282S%29%5E2
A=4S%5E2
A=%284%2F5%29R%5E2
A=%284%2F5%29%2825%29
A=20cm%5E2

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw this, the side of the square on the diameter is symmetric from the center, and let each part be x.
But the sides are now 2x each, so the vertical sides, extending to the semicircle, are 2x. The diagonal is the radius, or 5 cm. That is a right triangle.
x^2+(2x)^2=5^2=25
5x^2=25
x^2=5
x= +sqrt(5) cm.
2x= 2sqrt(5) cm.
The area of the square is twice x or [2(sqrt(5)]^2=4*5=20 cm^2