SOLUTION: A square is inscribed in a circle. If the side of the square is 4 what is the area and circumference of the circle.

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Question 258711: A square is inscribed in a circle. If the side of the square is 4 what is the area and circumference of the circle.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem, the diagonal of the inscribed square is the same as (equal to) the diameter of the circle.
The diagonal (D) of the square is:
D+=+sqrt%284%5E2%2B4%5E2%29 from the Pythagorean theorem.
D+=+sqrt%2832%29
D+=+4%2Asqrt%282%29
Now that you have the diameter of the circle, you can find its circumference (C) from:
C+=+%28pi%29D Substitute D+=+4%2Asqrt%282%29
C+=+%28pi%29%2A4%2Asqrt%282%29 or...
highlight%28C+=+4%28pi%29sqrt%282%29%29
The area (A) of the circle is:
A+=+%28pi%29%28D%2F2%29%5E2
A+=+%28pi%29%284%2Asqrt%282%29%2F2%29%5E2 Evaluate.
A+=+%28pi%29%2816%2A2%2F4%29
A+=+%28pi%29%2A8 or...
highlight%28A+=+8%28pi%29%29