We are asked to determine the area of the sector of a circle with a redius of 9 meters and an angle of 90 degrees. To do that we will use the following formula:
[tex]A=\frac{1}{2}r^2\theta[/tex]
Where:
[tex]\begin{gathered} r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]
We have that 90 degrees in radians are equivalent to:
[tex]\theta=\frac{\pi}{2}[/tex]
Substituting the values in the formula:
[tex]A=\frac{1}{2}(9m)^2(\frac{\pi}{2})[/tex]
Solving the operations:
[tex]A=\frac{81\pi}{4}\approx63.62m^2[/tex]
Therefore, the area is approximately 63.62 square meters.
