To find the area of a sector, you can use the following formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle of the sector in degrees,
- \( r \) is the radius.
Given:
- \( \theta = 135^\circ \)
- \( r = 13 , \text{in} \)
Plugging in the values:
\[ A = \frac{135}{360} \times \pi (13^2) \]
Calculating \( r^2 \):
\[ 13^2 = 169 \]
Now substituting that into the formula:
\[ A = \frac{135}{360} \times \pi \times 169 \]
Simplifying \( \frac{135}{360} \):
\[ \frac{135}{360} = \frac{3}{8} \]
Now substituting that back in:
\[ A = \frac{3}{8} \times \pi \times 169 \]
Now calculate:
\[ A \approx \frac{3}{8} \times 3.14159 \times 169 \approx \frac{3}{8} \times 530.143 \approx 199.3 , \text{in}^2 \]
Thus, the area of the sector is approximately:
\[ A \approx 199.1 , \text{in}^2 \]
The correct answer is:
A = 199.1 in²
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