To find the area of a sector, you can use the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( A \) is the area of the sector, \( \theta \) is the angle in degrees, and \( r \) is the radius.
Given:
- \( \theta = 135^\circ \)
- \( r = 13 \) inches
Substituting the values into the formula:
\[ A = \frac{135}{360} \times \pi \times (13^2) \]
First, calculate \( 13^2 \):
\[ 13^2 = 169 \]
Now substitute that back into the formula:
\[ A = \frac{135}{360} \times \pi \times 169 \]
Next, simplify \( \frac{135}{360} \):
\[ \frac{135}{360} = \frac{3}{8} \]
Now substituting this back:
\[ A = \frac{3}{8} \times \pi \times 169 \]
Now calculate the area:
\[ A \approx \frac{3}{8} \times 3.14159 \times 169 \approx \frac{3}{8} \times 530.1436 \approx 198.0364 \]
Now to round to one decimal place:
\[ A \approx 198.0 , \text{in}^2 \]
From the options provided, the closest one is:
\[ A \approx 199.1 , \text{in}^2 \]
Thus, the answer is:
A = 199.1 in².