SOLUTION: A Square with and area of 16 is partitioned into four congruent small squares. What is the area of the cirle that passes through the centers of the four similar squares?

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Question 34543: A Square with and area of 16 is partitioned into four congruent small squares. What is the area of the cirle that passes through the centers of the four similar squares?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) A square whose area is 16 has sides of 4.
2) If partitioned into four congruent squares, the smaller squares will have sides of 2.
3) The center of the smaller squares will be at a distance ofsqrt%282%29 from the center of the parent square.
4) The radius of the circle whose circumference contains the centers of the four smaller squares will besqrt%282%29.
5) The area of the circle is:
A+=+%28pi%29r%5E2
A+=+%28pi%29%28sqrt%282%29%29%5E2
A+=+2%28pi%29
If statement 3) is not obvious, here's how I determined that.
From the center of one of the smaller squares, drop a perpendicular to one of its sides thus bisecting that side. You will have formed a right triangle whose legs are 1 each and whose hypotenuse issqrt%282%29 (See Pythagorean theorem).
The hypotenuse is the radius of the circle.