The area of square fenced field is 576 ft^2. Find the area enclosed if we use the same fence to make a circle.

hala718 | Certified Educator

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 * piĀ = 733.39 ft^2

Then the area of the circular field will be 733.39 ft^2.

justaguide | Certified Educator

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

=> 48^2/pi

=> 2304/pi

The area of the circle is 2304/pi square feet.