Question

Write area f a circle as a function of circumfrence

Answer 1

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