SOLUTION: can you please help me solve ((( What is the area of a square inscribed in a circle with radius 6? )))

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Question 199048This question is from textbook geometry
: can you please help me solve ((( What is the area of a square inscribed in a circle with radius 6? ))) This question is from textbook geometry

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The inscribed square has a diagonal equal to 2 times the radius ( or the diameter) of the circle and this is 2*6 = 12.
If a square has a diagonal of 12, then you can find the length of its sides by using the Pythagorean theorem:
c%5E2+=+a%5E2%2Bb%5E2 Where c is the diagonal and, for a square, the two sides are equal and a = b, so...
c%5E2+=+a%5E2%2Ba%5E2
c%5E2+=+2a%5E2 Substitute c = 12 (the diameter of the circle).
12%5E2+=+2a%5E2
144+=+2a%5E2 Divide both sides by 2.
a%5E2+=+72
The area of the square with sides equal to a is:
A+=+a%5E2 Substitute a%5E2+=+72
highlight%28A+=+72%29sq.units.