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The problem asks to find the sector area of a circle, given:

- Radius \( r = 11 \, \text{ft} \)
- Central angle \( \theta = 150^\circ \)
- Use \( \pi = 3.14 \)

### Formula for the area of a sector:
\[
\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

### Step-by-step solution:
1. **Substitute the values**:
   \[
   \text{Area of sector} = \frac{150^\circ}{360^\circ} \times 3.14 \times (11)^2
   \]

2. **Simplify**:
   \[
   \frac{150^\circ}{360^\circ} = \frac{5}{12}
   \]
   So the area becomes:
   \[
   \text{Area of sector} = \frac{5}{12} \times 3.14 \times 121
   \]

3. **Calculate**:
   \[
   \frac{5}{12} \times 3.14 \times 121 \approx 0.4167 \times 3.14 \times 121
   \]
   \[
   \approx 0.4167 \times 380.74 = 158.57 \, \text{square feet}
   \]

### Final answer:
The sector area is approximately **158.6 square feet** (rounded to the nearest tenth).

Would you like further details on any of the steps?

Here are five related questions to explore:
1. How do you calculate the circumference of a circle?
2. What is the formula for the area of a full circle?
3. How do you convert degrees to radians, and how would that change this calculation?
4. What if the radius of the circle was doubled? How would the sector area change?
5. How do you calculate the length of the arc for the sector?

**Tip**: Remember that the sector area is proportional to the angle, so larger angles mean larger sectors for the same circle.

Find the sector area of the circle. Use 3.14 for the value of π. Round your answer to the nearest tenth. The radius is 11 ft, and the central angle is 150°.

Learn how to calculate the sector area of a circle with a 150° central angle and a radius of 11 ft. This geometry problem covers essential concepts and formulas related to circles and sectors, suitable for students in Grades 8-10.

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