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The problem shown in your image involves calculating the area of a sector of a circle, given an angle \(\theta = 150^\circ\) and a radius \(r = 24\) yards.

### Formula for the area of a sector:
The area \(A\) of a sector of a circle is given by the formula:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius.

### Plugging in the values:
\[
A = \frac{150^\circ}{360^\circ} \times \pi \times (24)^2
\]

Now let's calculate that.

The area of the lawn that receives water is approximately **754 square yards**, rounded to the nearest integer.

Would you like any further details or explanations?

Here are 5 related questions for further practice:
1. What would the area be if the angle was \(180^\circ\) instead of \(150^\circ\)?
2. How would the area change if the radius was doubled to 48 yards, keeping the same angle?
3. If the sector formed a complete circle (\(360^\circ\)), what would the area of the circle be?
4. How do you convert between degrees and radians for angular measurements?
5. What is the perimeter of this sector, including the arc length and the two radii?

**Tip:** The area of a sector is proportional to both the square of the radius and the size of the angle in degrees.

A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 150° and r = 24 yards.

This problem demonstrates how to calculate the area of a sector in a circle given an angle of 150 degrees and a radius of 24 yards using the formula A = (θ / 360) * π * r^2. Suitable for high school students, Grades 9-12.

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