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To solve the problem of finding the correct proportion for the sector area, we need to use the formula for the area of a sector of a circle.

### The formula for the area of a sector is:
\[
A = \pi r^2 \cdot \frac{\theta}{360^\circ}
\]
Where:
- \(A\) is the area of the sector
- \(r\) is the radius of the circle (11 feet here)
- \(\theta\) is the central angle of the sector (150° in this case)

### Setting up the proportion:
The fraction of the circle that this sector represents is \(\frac{150^\circ}{360^\circ}\). So the proportion to use would be:
\[
\frac{\text{Sector Area}}{\text{Total Circle Area}} = \frac{150}{360}
\]

Now, to find the actual area of the sector:
1. First, calculate the total area of the circle using the formula \(A_{\text{circle}} = \pi r^2\):
   \[
   A_{\text{circle}} = \pi \times (11)^2 = 121\pi \text{ square feet}
   \]
2. Use the proportion for the sector:
   \[
   A_{\text{sector}} = 121\pi \times \frac{150}{360} = 121\pi \times \frac{5}{12}
   \]
   Simplifying this expression will give the sector area.

Would you like to see the detailed steps for simplifying the final calculation or further clarifications?

### Relative Questions:
1. What is the total area of a circle with a different radius, like 15 feet?
2. How does the sector area change if the central angle is reduced to 90°?
3. Can you explain how the proportion \(\frac{150}{360}\) relates to the total circle?
4. What would be the area of a sector with a radius of 11 feet but a central angle of 180°?
5. How is the formula for sector area derived from the formula for the area of a full circle?

**Tip:** Always make sure that the angle \(\theta\) is in degrees (or radians, if required) when applying the sector area formula.

What is the correct proportion to use to solve for the sector area?

Find the correct proportion to solve for the sector area of a circle with a radius of 11 feet and a central angle of 150°. This problem covers key geometry concepts, including the formula for the area of a sector and proportional relationships in circles. Suitable for students in Grades 8-10.

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