To find the area of sector GPH with a radius of 12 yards and an angle of 20 degrees, you 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.
For your specific values:
- \(\theta = 20\) degrees,
- \(r = 12\) yards.
Now, plug in the values:
\[ \text{Area} = \frac{20}{360} \times \pi \times (12)^2 \]
First, calculate \(12^2\):
\[ 12^2 = 144 \]
So now we have:
\[ \text{Area} = \frac{20}{360} \times \pi \times 144 \]
Next, simplify \(\frac{20}{360}\):
\[ \frac{20}{360} = \frac{1}{18} \]
Now substitute this back into the equation:
\[ \text{Area} = \frac{1}{18} \times \pi \times 144 \]
Now calculate:
\[ \frac{144}{18} = 8 \]
Thus, the area becomes:
\[ \text{Area} = 8\pi \]
If you want a numerical approximation, using \(\pi \approx 3.14\):
\[ \text{Area} \approx 8 \times 3.14 \approx 25.12 \text{ square yards} \]
So, the area of sector GPH is:
\[ 8\pi \text{ square yards} \quad \text{or} \quad \approx 25.12 \text{ square yards} \]