[tex]circumference = 2\pi \times r[/tex]
[tex]area = \pi {r}^{2} [/tex]
we want area =circumference*something
dividing our first equation by 2*pi
[tex] \frac{circumference}{2\pi} = r[/tex]
substituting in the second equation
[tex]area = \pi { (\frac{circumference}{2\pi}) }^{2} [/tex]
simplifying
[tex]area = \pi(\frac{ {circumference}^{2} }{4 {\pi}^{2} } )[/tex]
[tex]area = \frac{{circumference} ^{2} }{4\pi} [/tex]
