Answer:
1330.81 square feet
Explanation:
In the circle, there are two unshaded sectors with central angles 26° and 90°.
The sum of the central angles = 360°.
Therefore, the sum of the central angle of the shaded sectors will be:
[tex]360\degree-(26\degree+90\degree)=244\degree[/tex]
The area of a sector is calculated using the formula:
[tex]A=\frac{\theta}{360\degree}\times\pi r^2\text{ where }\begin{cases}Central\; Angle,\theta=244\degree \\ Radius,r,HK=25ft\end{cases}[/tex]
Substitute the values into the formula:
[tex]\begin{gathered} A=\frac{244}{360}\times\pi\times25^2 \\ =1330.8136 \\ \approx1330.81\; ft^2 \end{gathered}[/tex]
The area of the shaded sector is 1330.81 square feet (rounded to the hundredth place).
