Sector

Let $A$ be the shaded area, $B$ be the area of the square, $C$ be the area of the circle, and $s$ be the side length of the square. $C = \pi r^2 = 4\pi \\ A = \frac{C}{4} = \pi \\ B = 3A = 3\pi \\ s = \sqrt{B} = \sqrt{3\pi}$ Therefore $x = 2$ and $y = 3,$ so $x+y=\boxed{5}$

The shaded part is quarter of a circle. So the area is $\dfrac{1}{4}\pi (2^2)=\pi$ . Let $a$ be the side length of the square.

$A_{shaded}=\dfrac{1}{3}A_{square}$

$\pi=\dfrac{1}{3}(a^2)$

$3\pi=a^2$

$a=\sqrt{3\pi}$

Therefore, $x=2$ and $y=3$ .

The desired answer is $2+3=$ $\boxed{5}$

90/360 pi 2^2=1/3x^2 where x is the side length of the square.