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?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\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?
train