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To solve for the area of the sector, we can use a proportion based on the fraction of the circle represented by the sector's central angle.

The formula for the area \( A_{\text{sector}} \) of a sector of a circle is:

\[
A_{\text{sector}} = \frac{\theta}{360^\circ} \times A_{\text{circle}}
\]

Where:
- \( \theta \) is the central angle of the sector in degrees.
- \( A_{\text{circle}} = \pi r^2 \) is the area of the full circle with radius \( r \).

From the image:
- \( \theta = 150^\circ \)
- Radius \( r = 11 \, \text{ft} \)

Thus, the correct proportion is:

\[
\frac{A_{\text{sector}}}{A_{\text{circle}}} = \frac{150^\circ}{360^\circ}
\]

This simplifies to:

\[
A_{\text{sector}} = \frac{150^\circ}{360^\circ} \times \pi \times (11^2)
\]

Let me know if you would like the detailed steps to calculate the area or if you have any questions!

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Here are some related questions for further practice:

1. How would the formula change if the angle was given in radians?
2. What would the area of the entire circle be?
3. What proportion would you use for a sector with a \( 90^\circ \) angle?
4. How does the sector area change if the radius is doubled?
5. What is the area of a sector with a central angle of \( 45^\circ \) and radius \( 8 \, \text{ft} \)?

**Tip:** Always ensure that the angle you use in sector formulas is in the correct units (degrees or radians).

What is the correct proportion to use to solve for the sector area of a circle with a radius of 11 ft and a central angle of 150°?

Learn how to find the correct proportion to solve for the area of a sector with a central angle of 150° and a radius of 11 feet. This problem covers key geometry concepts like sector area and circle properties.

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