Circle vs. Square

If $r$ is the radius of the circle and $x$ the side length of the square, then we are given that

$2\pi r = 4x \Longrightarrow x = \dfrac{\pi}{2}r \Longrightarrow x^{2} = \left(\dfrac{\pi}{2}\right)^{2}r^{2}.$

But since $\pi \lt 4$ we know that $\left(\dfrac{\pi}{2}\right)^{2} = \dfrac{\pi^{2}}{4} \lt \dfrac{\pi^{2}}{\pi} = \pi$ , and so

$x^{2} = \left(\dfrac{\pi}{2}\right)^{2}r^{2} \lt \pi r^{2}$ ,

i.e., with the given condition, the area of the circle will be greater than that of the square.

a(side of square)=11r(radius of cirle)/7 therefore area of circle=3.1r(square) and area of square=2.4r(square)