To find the area of sector JKL in circle K, we can use the formula for the area of a sector, which is given by:
\[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \]
where \(\theta\) is the angle of the sector in degrees and \(r\) is the radius of the circle.
In this problem, we have:
- \(m \angle JKL = 46^\circ\)
- The length \(JK = 11\), which acts as the radius \(r\) of the circle since all radii in a circle measure the same.
Now, substituting the known values into the formula:
-
Identify \(\theta\) and \(r\):
- \(\theta = 46^\circ\)
- \(r = 11\)
-
Plugging in the values:
\[ \text{Area} = \frac{46}{360} \times \pi \times 11^2 \]
- Calculate \(11^2\):
\[ 11^2 = 121 \]
- Substitute back into the area equation:
\[ \text{Area} = \frac{46}{360} \times \pi \times 121 \]
- Calculate \(\frac{46}{360}\):
\[ \frac{46}{360} = \frac{23}{180} \approx 0.12777778 \]
- Then equation now looks like this:
\[ \text{Area} \approx 0.12777778 \times \pi \times 121 \]
- Now compute the multiplication:
\[ \text{Area} \approx 0.12777778 \times 3.14159 \times 121 \]
\[ \text{Area} \approx 0.12777778 \times 380.1321 \approx 48.63785 \]
- Finally, rounding to the nearest hundredth:
\[ \text{Area} \approx 48.64 \]
Thus, the area of sector JKL is approximately 48.64 square units.