Answer:
[tex]251.2 ft^2[/tex]
Step-by-step explanation:
In this problem we want to find the area of a ring-shaped region.
The inner radius of the ring is
[tex]r_i = 8 ft[/tex]
while the outer radius of the ring is
[tex]r_o=12 ft[/tex]
The area of the ring is equal to the area of the larger circle minus the area of the smaller circle.
The area of the larger circle is:
[tex]A_o = \pi r_o^2 = \pi (12)^2=452.16 ft^2[/tex]
The area of the smaller circle is instead
[tex]A_i=\pi r_i^2 = \pi (8)^2=200.96 ft^2[/tex]
Therefore, the area of the ring is:
[tex]A=A_o-A_i=452.16-200.96=251.2 ft^2[/tex]
