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

A=530.9 in.2
upper A equals 530.9 in. squared

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

A=30.6 in.2

Answer 1

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.