The area of a circle is given by the following formula:
[tex]A=\pi r^2[/tex]
Where r is the radius of the circle.
To calculate the area of this circular sector, we can use the following rule of three:
[tex]\begin{gathered} \text{central angle}\to\text{ area} \\ 360\degree\to\pi r^2 \\ 135\degree\to x \end{gathered}[/tex]
From this rule of three, we can write the following proportion and solve for x:
[tex]\begin{gathered} \frac{360}{135}=\frac{\pi r^2}{x} \\ x\cdot360=\pi r^2\cdot135 \\ x=\pi r^2\cdot\frac{135}{360} \\ x=3.14\cdot65^2\cdot\frac{135}{360} \\ x=4974.9 \end{gathered}[/tex]
Therefore the correct option is B.
