Question

In circle L with m, angle, K, L, M, equals, 46, degreesm∠KLM=46
∘
and K, L, equals, 13KL=13, find the area of sector KLM. Round to the nearest hundredth.

Answer 1

To find the area of sector KLM, you can use the formula for the area of a sector of a circle:

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

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

Here, we are given:
- \( \theta = 46^\circ \)
- \( KL = 13 \) (which represents the radius \( r \) of the circle, since the points K and L are on the circle)

Now, plug in the values into the formula:

\[
\text{Area of sector KLM} = \frac{46}{360} \times \pi \times (13^2)
\]

Calculating \( 13^2 \):

\[
13^2 = 169
\]

Now, substituting this back into the formula:

\[
\text{Area of sector KLM} = \frac{46}{360} \times \pi \times 169
\]

Next, simplify \( \frac{46}{360} \):

\[
\frac{46}{360} \approx 0.12778
\]

Now we can find the area:

\[
\text{Area of sector KLM} \approx 0.12778 \times \pi \times 169
\]

Using \(\pi \approx 3.14159\):

\[
\text{Area of sector KLM} \approx 0.12778 \times 3.14159 \times 169
\]

Calculating that:

\[
\text{Area of sector KLM} \approx 0.12778 \times 530.141
\]

Calculating this gives:

\[
\text{Area of sector KLM} \approx 67.66
\]

Rounding to the nearest hundredth, we find:

\[
\text{Area of sector KLM} \approx 67.66
\]

Thus, the area of sector KLM is approximately **67.66 square units**.