What is the area of a circle with a circumference of 30 feet?

Exact Area =  225/pi

Approximate Area = 71.65605

The approximate value is using pi = 3.14; I rounded to the five decimal places. The units for the area are in square feet, which can be written as "sq ft" or "ft^2" without quotes.

Explanation:

C = 30 is the circumference

C = 2*pi*r ... is the circumference in general

Equate the two right hand sides and isolate r

2pi*r = 30

r = 30/(2pi)

r = 15/pi

This is the exact radius in terms of pi

Plug this into the area formula to get...

A = pi*r^2

A = pi*( r )^2

A = pi*( 15/pi )^2

A = pi*( 225/(pi^2) )

A = 225/pi

This is the exact area in terms of pi. If your teacher wants the exact answer, and only this, then you can stop here.

If your teacher wants you to use pi = 3.14 as the approximation, then we'll get an approximate area of roughly A = 225/pi = 225/3.14 = 71.65605 square feet. Use more decimal digits in pi to get a better approximation.