The formula for area of a sector, A, is given below as,
[tex]\text{Area of a sector, A =}\frac{\theta}{360^0}\times\pi r^2[/tex]
Where,
[tex]\begin{gathered} r\text{ is the radius} \\ \theta\text{ is the angle subtended by the arc} \\ r=4\text{ miles} \\ \theta=135^0 \\ \pi=3.14 \end{gathered}[/tex]
Substituting the variables into the formula for the area of a sector given above,
[tex]\begin{gathered} A=\frac{\theta}{360^0}\times\pi r^2 \\ \Rightarrow\frac{135^0}{360^0}\times3.14\times\times(4)^2=18.84mi^2 \end{gathered}[/tex]
The simplest form of the area of the sector, A, is 18.8mi² (one decimal palce).
