Answer:
[tex]\boxed{A=\dfrac{169}{4}\pi\ \text{ ft}^2}[/tex]
Step-by-step explanation:
We know the following formulas regarding circles:
- [tex]C=2\pi r[/tex]
- [tex]A=\pi r^2[/tex]
where [tex]r[/tex] is the circle's radius and [tex]\pi[/tex] is a constant [tex]\approx 3.14159[/tex].
We are given the circumference of a circle:
Plugging this into the first equation, we can solve for r:
[tex]13\pi = 2\pi r[/tex]
↓ dividing both sides by [tex]2\pi[/tex]
[tex]\dfrac{13}{2} = r[/tex]
We can now solve for area using this r-value:
[tex]A=\pi r^2[/tex]
[tex]A=\pi (13/2)^2[/tex]
[tex]\boxed{A=\dfrac{169}{4}\pi\ \text{ ft}^2}[/tex]
