Final answer:
To find the area of a circle with a given circumference, we can use the formula A = πr². By solving the equation 15π = 2πr, we can find the radius. Substituting this radius into the area formula gives us an area of 56.25π square feet.
Step-by-step explanation:
To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius.
In this case, we are given the circumference of the circle, which is 15π ft.
The formula for circumference is C = 2πr, so we can write the given circumference as 15π = 2πr.
We can solve this equation to find the value of r, and then substitute it into the area formula to find the area.
Dividing both sides of the equation by 2π, we get 15π/2π = r. Simplifying, we have 15/2 = r.
Therefore, the radius is 15/2 = 7.5 ft.
Now we can substitute this value of r into the area formula. A = π(7.5)^2 = 56.25π ft². So, the area of the circle is 56.25π square feet.