find the area of the shaded region

Explanation:

Step1: Recall area - of - a - sector formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.

Step2: Identify values of $\theta$ and $r$

Given that $\theta = 135^{\circ}$ and $r = 9m$.

Step3: Substitute values into the formula

$A=\frac{135^{\circ}}{360^{\circ}}\times\pi\times(9)^{2}$. First, simplify $\frac{135}{360}=\frac{3}{8}$. Then, $(9)^{2}=81$. So, $A=\frac{3}{8}\times\pi\times81=\frac{243\pi}{8}m^{2}\approx\frac{243\times3.14}{8}=\frac{763.02}{8}=95.3775m^{2}$.

Answer:

$\frac{243\pi}{8}m^{2}\approx95.38m^{2}$