2004 AIME I Problems/Problem 4

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A square has sides of length 2. Set $S$is the set of all line segments that have length 2 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set $S$ enclose a region whose area to the nearest hundredth is $k.$ Find $100k.$


This problem needs a solution. If you have a solution for it, please help us out by adding it. The region is the inscribed circle of the square, so the area is $\pi$, or to the nearest hundreth $3.14$ and so the answer is 314.

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