smc

Let's say the circle has a circumference ( or perimeter of $4\pi$). Since the perimeter of the square is the same as the perimeter of the circle, the side length of the square is $\pi$. That means that the area of the square is ${\pi }^2$. The area of the circle is $4\pi$. So the area of the circle over the area of the square is $\frac{4\pi }{{\pi }^2}\Rightarrow \frac{4}{\pi }\Rightarrow$ $\boxed{\frac{4}{\pi }}$