SOLUTION: Find the area of a square inscribed in a circle whose radius is 8cm. Thank you

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Question 1161383: Find the area of a square inscribed in a circle whose radius is 8cm. Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The area of this square is 128 square centimeters.

Drawing the figure, center to any corner is 8, and is hypotenuse of a 45-45-90 right triangle. If v is one of the legs then v%5E2%2Bv%5E2=8%5E2.
.
.
v=4sqrt%282%29

Each side or dimension for the square is 2v=8sqrt%282%29.

Area:
%288sqrt%282%29%29%5E2
64%2A2
highlight%28128%29 squarecentimeters

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area of a square inscribed in a circle whose radius is 8cm. Thank you
With the radius being 8 cm, the diameter is 2(8) = 16 cm.

The diagonal of a square inscribed in a circle is also the circle's diameter.

The legs/sides of the square are congruent - this being a square - so with each congruent side being S, we get: 

The above, highlight_green%28matrix%281%2C5%2C+S%5E2%2C+%22%2C%22%2C+or%2C+128%2C+cm%5E2%29%29 represents the AREA of the square.