For this case we have to:
If Sergio has 72 feet of fence then we have that the circumference of the fence (whose space is circular) is 72.
By definition, the circumference of a circle is given by:
[tex]C = \pi * d[/tex]
Where:
d: It is the diameter of the circumference
So:
[tex]72 = \pi * d\\d = \frac {72} {\pi}\\d = \frac {72} {3.14}\\d = 22.93 \ ft[/tex]
Then, the radius will be given by: r = 11.45 \ ft
Thus, the area of the circular portion will be:
[tex]A = \pi * r ^ 2\\A = 3.14 * (11.45) ^ 2\\A = 3.14 * 131.1025\\A = 411.66 \ ft ^ 2[/tex]
Thus, the area of the playing space is:[tex]A = 411.66 \ ft ^ 2[/tex]
Answer:
[tex]A = 411.66 \ ft ^ 2[/tex]
