SOLUTION: a square is inscribed in a circle. If the area of the circle is 25π sq. mm, what is the area of the square?

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Question 1141716: a square is inscribed in a circle. If the area of the circle is 25π sq. mm, what is the area of the square?
Found 3 solutions by Boreal, josmiceli, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
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The circle has radius 5 cm for an area of 25*pi mm^2.
If one draws this, a right triangle may be formed with one leg the radius of the circle, the second leg 1/2 the side of the square, and the hypotenuse half the diagonal of the square.
Because that triangle is a 45-45-90 triangle, half the side of the square is 5 cm as well and the area of the square is 100cm^2, (10 cm)^2.

Answer by josmiceli(19441) About Me  (Show Source):
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The diagonal of the square will be the same as
the diameter of the circle
+A+=+25pi+
+A+=+pi%2Ar%5E2+
+25pi+=+pi%2Ar%5E2+
+r%5E2+=+25+
+r+=+5+
This is half the diameter, so
diameter = +10+, and the
diagonal also = +10+
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Let +x+ = a side of the square
For a square
+10+=+sqrt%282%29%2Ax+
+x+=+10%2Fsqrt%282%29+
+x+=+10%2Asqrt%282%29+%2F+2+
+x+=+5%2Asqrt%282%29+
and
Area of square = +x%5E2+
+x%5E2+=+25%2A2+
+x%5E2+=+50+ mm2
get a 2nd opinion if needed

Answer by MathTherapy(10557) About Me  (Show Source):
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a square is inscribed in a circle. If the area of the circle is 25π sq. mm, what is the area of the square? 
Is there EVER a day when most of these people DON'T give wrong answers?

The area of the square is NOT 100 mm2, but 50 mm2 instead.