Question

Using the formula for the area of a sector, solve for the area of a sector with an angle of 135° and a radius of 13 in.(1 point)
Responses

A=199.1 in.2
upper A equals 199.1 in. squared

A=398.2 in.2
upper A equals 398.2 in. squared

A=30.6 in.2
upper A equals 30.6 in. squared

A=530.9 in.2

Answer 1

To find the area of a sector, you can use the following formula:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle in degrees,
- \( r \) is the radius of the circle.

Given:
- \( \theta = 135^\circ \)
- \( r = 13 \) in.

Now, plugging the values into the formula:

\[
A = \frac{135}{360} \times \pi \times (13)^2
\]

Calculating \( 13^2 \):

\[
13^2 = 169
\]

Now substitute that back into the equation:

\[
A = \frac{135}{360} \times \pi \times 169
\]

Now simplify \( \frac{135}{360} \):

\[
\frac{135}{360} = \frac{3}{8} \quad (\text{after dividing both the numerator and denominator by 45})
\]

Now, substitute this back into the area formula:

\[
A = \frac{3}{8} \times \pi \times 169
\]

Now calculate \( \frac{3}{8} \times 169 \):

\[
\frac{3 \times 169}{8} = \frac{507}{8} = 63.375
\]

Now multiply by \( \pi \):

\[
A \approx 63.375 \times 3.14159 \approx 199.1 \text{ in}^2
\]

Thus, the area of the sector is approximately

\[
\boxed{199.1 \text{ in}^2}
\]

The correct response is: **A=199.1 in.²**.