The area of a circular sector with angle θ and radius r is given by:
[tex]A(\theta,r)=\pi\cdot r^2\cdot(\frac{\theta}{2\pi})=\frac{\theta}{2}\cdot r^2\text{.}[/tex]In this case, we have:
• r = 12.0ft,
,• θ = 2pi/3.
Replacing these data in the equation above, we get:
[tex]A(\frac{2\pi}{3},12.0ft)=\frac{\frac{2\pi}{3}}{2}\cdot(12.0ft)^2=\frac{\pi}{3}\cdot144\cdot ft^2\cong150.8ft^2.[/tex]Answer: 150.8ft²
