Answer
$2\pi$ square units
Work Step by Step
The area of the shaded region is equal to the area of the circle.
To find the are of the circle, we need to the length of either radius or diameter of the circle.
The side length of the square is
$s=2$.
The diagonal of a square is $s\sqrt2$ units where $s$ is the side length.
$=s\sqrt2$
$=2\sqrt2$
The length of the diagonal is equal to the diameter of the circle.
Thus, the diameter of the circle is $d=2\sqrt2$.
The Area of a circle is given by the formula
$A=\pi \left(\frac{d}{2}\right)^2$
Substitute the value of $d$.
$A=\pi \left(\frac{2\sqrt2}{2}\right)^2$
$A=\pi (2)$
$A=2\pi$ square units
Hence, the area of the shaded region is $2\pi$ square units.
