To find the area of a sector of a circle, we 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,
- \(r\) is the radius of the circle.
For this problem, we have:
- \(\theta = 135^\circ\)
- \(r = 13 , \text{in.}\)
Substituting the values into the formula:
\[ A = \frac{135}{360} \times \pi (13)^2 \]
Calculating \(r^2\):
\[ (13)^2 = 169 \]
Now substituting this value back into the equation:
\[ A = \frac{135}{360} \times \pi \times 169 \]
Calculating \(\frac{135}{360}\):
\[ \frac{135}{360} = \frac{15}{40} = \frac{3}{8} \]
So now we have:
\[ A = \frac{3}{8} \times \pi \times 169 \]
Using \(\pi \approx 3.14\):
\[ A \approx \frac{3}{8} \times 3.14 \times 169 \]
Calculating \(3.14 \times 169\):
\[ 3.14 \times 169 \approx 530.46 \]
Now multiply by \(\frac{3}{8}\):
\[ A \approx \frac{3}{8} \times 530.46 \approx 198.2 \]
So, approximately:
\[ A \approx 199.1 , \text{in}^2 \]
The answer is:
\[ A = 199.1 , \text{in}^2 \]
Thus, the correct response is:
A = 199.1 in.²
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