Answer:[tex]\frac{14\pi}{3}mi^2[/tex]Explanation:
The area of a sector is given as:
[tex]\begin{gathered} Area\text{ = }\frac{\theta}{360}\times\pi r^2 \\ \\ \end{gathered}[/tex]
The sector angle, θ = 360° - 255°
θ = 105°
The radius, r = 4 mi
Substitute these values into the equation to solve for the area
[tex]\begin{gathered} Area=\frac{105}{360}\times\pi\times4^2 \\ \\ Area=\frac{105}{360}\times16\pi \\ \\ Area=\frac{7}{24}\times16\pi \\ \\ Area=\frac{7}{3}\times2\pi \\ \\ Area=\frac{14\pi}{3}mi^2 \\ \end{gathered}[/tex]
