Question

In circle G with m, angle, F, G, H, equals, 82, degreesm∠FGH=82
∘
and F, G, equals, 13FG=13, find the area of sector FGH. Round to the nearest hundredth.

Answer 1

To find the area of sector \( FGH \) in circle \( G \), we can use the formula for the area of a sector:

\[
\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

where \( \theta \) is the angle in degrees and \( r \) is the radius of the circle.

From the problem, we have:
- \( m∠FGH = 82^\circ \)
- \( FG = 13 \), which we will assume is the radius \( r \) (i.e., \( r = 13 \)).

Now, we can substitute these values into the formula:

\[
\text{Area of sector} = \frac{82}{360} \times \pi \times (13)^2
\]

First, calculate \( (13)^2 \):

\[
(13)^2 = 169
\]

Next, calculate the area:

\[
\text{Area of sector} = \frac{82}{360} \times \pi \times 169
\]

Now, calculate \( \frac{82}{360} \):

\[
\frac{82}{360} \approx 0.2278
\]

Now multiply by \( \pi \) and \( 169 \):

\[
\text{Area of sector} \approx 0.2278 \times \pi \times 169 \approx 0.2278 \times 531.681 \approx 121.03
\]

Now, rounding to the nearest hundredth, the area of sector \( FGH \) is approximately:

\[
\boxed{121.03}
\]