A unit square is rotated $45^\circ$ about its center.  What is the area of the region swept out by the interior of the square?
Question:
A unit square is rotated $45^\circ$ about its center.  What is the area of the region swept out by the interior of the square?
Answer:
Let's think step by step.

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\frac \pi4 + 2 - \sqrt2
A unit square is rotated $45^\circ$ about its center.  What is the area of the region swept out by the interior of the square?
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