The area of a square fence is 576 square feet. The area of a square is s^2 where s is the side.
s^2 = 576
=> s = 24
The perimeter of the square is 96.
For a circle of radius r the circumference is 2*pi*r and the area is pi*r^2.
As the same fence is used to build the circle
2*pi*r = 96
r = 48/pi
The area = pi*(48/pi)^2
=> pi*48^2 / pi^2
The area of the circle is 2304/pi square feet.
Given that the area of the square field is 576 ft^2
Then, we will calculate the length of the sides.
Let the side of the field be x.
==> A= x^2 = 576
==> x = 24
Now we will calculate the perimeter of the fence .
==> P = 4*x = 4*24 = 96
Then the circumference of the circle will be 96 ft.
Now we will calculate the radius.
==> c = 2*pi * r = 96
==> r = 96/2pi = 15.28 ft.
Now we will calculate the area.
==> A = r^2 * pi = 15.28^2 * pi = 733.39 ft^2
Then the area of the circular field will be 733.39 ft^2.