The area \( A \) of a sector of a circle can be calculated using the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( \theta \) is the angle of the sector in degrees, and \( r \) is the radius of the circle.
Given:
- \( \theta = 135^\circ \)
- \( r = 13 \) in.
Let's substitute the values into the formula:
\[ A = \frac{135}{360} \times \pi (13)^2 \]
First, calculate \( (13)^2 \):
\[ (13)^2 = 169 \]
Now substitute this into the area formula:
\[ A = \frac{135}{360} \times \pi \times 169 \]
Now simplify \( \frac{135}{360} \):
\[ \frac{135}{360} = \frac{135 \div 45}{360 \div 45} = \frac{3}{8} \]
Now we can write the formula as:
\[ A = \frac{3}{8} \times \pi \times 169 \]
Next, calculate \( A \) using \( \pi \approx 3.14159 \):
\[ A \approx \frac{3}{8} \times 3.14159 \times 169 \]
Calculating \( 3.14159 \times 169 \):
\[ 3.14159 \times 169 \approx 531.8 \]
Now multiply by \( \frac{3}{8} \):
\[ A \approx \frac{3}{8} \times 531.8 \approx 199.1 \]
Thus, the area of the sector is approximately:
\[ \boxed{199.1 \text{ in}^2} \]
The correct response is:
A = 199.1 in.².