# What is the area of a circle in terms of circumference?

Oct 1, 2015

The circumference can be written as $P = 2 \pi r$

#### Explanation:

So the radius is $r = \frac{P}{2 \pi}$

And since the area is $A = \pi {r}^{2}$

We can rewrite this as:

$A = \pi {\left(\frac{P}{2 \pi}\right)}^{2} = \cancel{\pi} \cdot \left({P}^{2} / \left(4 \cdot \pi \cdot \cancel{\pi}\right)\right) = {P}^{2} / \left(4 \pi\right)$