To find the area of sector \( GPH \), we can use the formula for the area of a sector:
\[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \]
where:
- \( \theta \) is the angle in degrees,
- \( r \) is the radius.
From your description, it appears that the radius \( r \) is 15 yards and the angle \( \theta \) is 40 degrees.
Now, substituting the values into the formula:
\[ \text{Area} = \frac{40}{360} \times \pi (15)^2 \]
First, simplify \( \frac{40}{360} \):
\[ \frac{40}{360} = \frac{1}{9} \]
Now calculate \( 15^2 \):
\[ 15^2 = 225 \]
Substitute back into the area formula:
\[ \text{Area} = \frac{1}{9} \times \pi \times 225 \]
\[ \text{Area} = \frac{225\pi}{9} \]
\[ \text{Area} = 25\pi \]
Thus, the area of sector \( GPH \) is
\[ 25\pi \text{ square yards} \]
If you want a numerical approximation, using \( \pi \approx 3.14 \):
\[ 25\pi \approx 25 \times 3.14 \approx 78.5 \text{ square yards} \]
So the area is approximately \( 78.5 \text{ square yards} \).