SOLUTION: A square is inscribed inside a quadrant of a circle of radius 10 cm. Calculate the area of the square.

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Question 287595: A square is inscribed inside a quadrant of a circle of radius 10 cm. Calculate the area of the square.
Answer by dabanfield(803) About Me  (Show Source):
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The diagonal of the square is the radius of the circle. The diagonal of the square is also the hypotenuse of an isosceles triangle. Let x be the length of the sides. Then by the Pythagorean Theorem we have:
x^2 + x^2 = 10^2
2*x^2 = 100
x^2 = 50
But x^2 is also the area of the square.