Solution:
We are required to find the area of the sector given in the question.
The area of a sector can be calculated by the formula
[tex]\begin{gathered} A=\frac{\theta}{360}\pi r^2 \\ \text{Where }\theta=angle\text{ subtended by the sector at the center} \\ r=\text{radius of the sector} \end{gathered}[/tex][tex]\begin{gathered} \text{For this question, } \\ \theta=\frac{1}{4}(360)=270^0 \\ r=4m \end{gathered}[/tex][tex]\begin{gathered} A=\frac{270}{360}\text{ x 3.14 x 4 x 4} \\ \\ A=37.68m^2 \\ A=37.7m^2\text{(nearest tenth)} \\ \\ \text{Thus, the area of the sector is 37.7m}^2\text{ (nearest tenth)} \end{gathered}[/tex]
