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It is easy to show this graphically but, given the limitations of this browser, an algebraic explanation is the best that I can do.
Suppose the sides of the square are x inches.
Then, by Pythagoras, the diameter is sqrt(x2 + x2) = sqrt(2x2) = x*sqrt(2) inches
ie x*sqrt(2) = 10 or x = 10/sqrt(2) = 5*sqrt(2)
Then area = x2 = 25*2 = 50 square inches.
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