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The problem in the image asks to find the area of the sector of a circle with a radius of 11 feet and a central angle of 150°. We're instructed to use 3.14 for the value of \(\pi\) and round the answer to the nearest tenth.

The formula for the area of a sector is:

\[
\text{Sector Area} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta = 150^\circ\) (central angle),
- \(r = 11\) feet (radius),
- \(\pi \approx 3.14\).

Let's calculate the area step by step.

1. Compute the area of the entire circle:
   \[
   \text{Area of circle} = \pi r^2 = 3.14 \times (11)^2 = 3.14 \times 121 = 379.94 \, \text{square feet}.
   \]

2. Now, find the fraction of the circle corresponding to the sector (since 150° is out of 360°):
   \[
   \text{Sector Area} = \frac{150}{360} \times 379.94 = 0.4167 \times 379.94 = 158.31 \, \text{square feet}.
   \]

Therefore, the area of the sector is approximately **158.3 square feet** (rounded to the nearest tenth).

Would you like more details or have any questions?

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Here are some related questions to explore:
1. How do you find the area of a sector if the angle is given in radians?
2. What is the relationship between the radius and the area of a circle?
3. How does increasing the angle \(\theta\) affect the sector area?
4. Can we use a different approximation of \(\pi\) to improve the accuracy?
5. How would the calculation change if the radius were doubled?

**Tip:** Always make sure the angle \(\theta\) is in degrees when using the formula for sectors, unless you're using radians for a specific formula!

Find the sector area of a circle with a radius of 11 feet and a central angle of 150°. Use 3.14 for the value of π and round the answer to the nearest tenth.

Learn how to calculate the area of a sector of a circle with a radius of 11 feet and a central angle of 150°. This problem uses the formula for the area of a sector and covers key geometry concepts. Suitable for students in Grades 8-10.

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