The circumference (C) of a circle with radius r is:
[tex]C=2\pi r[/tex]Given the measure of the circumference (13π in), first, let's substitute it in the equation find r:
[tex]\begin{gathered} 13\pi=2\pi r \\ \text{ Dividing both sides by 2}\pi\text{:} \\ \frac{13\pi}{2\pi}=\frac{2\pi}{2\pi}r \\ \frac{13}{2}=r \\ r=\frac{13}{2}\text{ in} \end{gathered}[/tex]The area (A) of a circumference with radius r is:
[tex]A=\pi r^2[/tex]Knowing r, substitute it to find A:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi *(\frac{13}{2})^2 \\ A=42.25\text{ in}^2 \end{gathered}[/tex]Answer: Area = 42.25 in².
