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2013 AMC 10A Problem 20

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2013 AMC 10A Problem 20AMC 10 Step by Step
Name:                             Date: September 13, 2026
Transformations & Symmetry · difficulty 4 of 5 · about 8 min · position P16-20

A unit square is rotated 45∘45^\circ about its center. What is the area of the region swept out by the interior of the square?

  1. A)

    1−22+π41 - \frac{\sqrt2}{2} + \frac{\pi}{4}

  2. B)

    12+π4\frac{1}{2} + \frac{\pi}{4}

  3. C)

    2−2+π42 - \sqrt2 + \frac{\pi}{4}

  4. D)

    22+π4\frac{\sqrt2}{2} + \frac{\pi}{4}

  5. E)

    1+24+π81 + \frac{\sqrt2}{4} + \frac{\pi}{8}

Working