The circumference of a circle with radius r is given by 2*pi*r. The area of a circle with radius r is pi*r^2.
Here, circumference is 24*pi = 2*pi*r
=> r = 24*pi / 2*pi
=> r = 12
The area of the circle is pi*r^2 = pi*12^2 = pi*144
The required area is pi*144
Given the circumference of a circle is 24 pi.
We will use the circumference formula to find the radius.
We know that C = 2*pi* r = 24*pi
==> r = 24pi/2pi = 12
Then the radius is 12.
Now we will calculate the area of the the circle.
==> A + r^2 * pi = 12^2 * pi = 144pi = 452.39
Then the area of the circle is A= 144pi = 452.39 square units.