Question

What is the area of sector​ GPH?
font size increased by 1 font size decreased by 1 font size decreased by 1 12 yd12 yd20 degrees20°Upper HHUpper GGUpper PP

Answer 1

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:

\[
8\pi \text{ square yards} \quad \text{or} \quad \approx 25.12 \text{ square yards}
\]