2013 AMC 10A Question 20
AMC10 · 2013 AMC 10A
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?
$1 - \dfrac{\sqrt2}{2} + \dfrac{\pi}{4}$
$\dfrac{1}{2} + \dfrac{\pi}{4}$
$2 - \sqrt2 + \dfrac{\pi}{4}$
$\dfrac{\sqrt2}{2} + \dfrac{\pi}{4}$
$1 + \dfrac{\sqrt2}{4} + \dfrac{\pi}{8}$