Answer
The area of a circle expressed in terms of its circumference can be expressed by the following function:
$A$ = $\frac{C^{2}}{4\pi}$
Work Step by Step
The circumference of a circle is expressed as:
$C$ = $2\pi$$r$
Since we need to know $r$ for our area formula, we can isolate $r$ by dividing both sides of the equation by $2\pi$. We then get:
$r$ = $\frac{C}{2\pi}$
The area of a circle is given by the following formula:
$A$ = $\pi$$r^{2}$
We have the value of $r$ already expressed in terms of $C$, so we can substitute what we have for $r$ into the equation for the area of the circle:
$A$ = $\pi$$(\frac{C}{2\pi})^{2}$
We simplify to get:
$A$ = $\pi$$\frac{C^{2}}{4\pi^{2}}$
We cross-cancel the $\pi$ term to get the area of the circle expressed in terms of its circumference:
$A$ = $\frac{C^{2}}{4\pi}$
