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=30.6 in.2 upper A equals 30.6 in. squared A=398.2 in.2 upper A equals 398.2 in. squared A=530.9 in.2

Answer 1

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.

In this case, you have:
- \( \theta = 135° \)
- \( r = 13 \) in.

Now plug the values into the formula:

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

First, calculate \( (13)^2 \):

\[
(13)^2 = 169
\]

Now substitute this value back into the formula:

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

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

\[
\frac{135}{360} = \frac{135 \div 45}{360 \div 45} = \frac{3}{8}
\]

Now, substitute:

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

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

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

Now multiply by \( \pi \):

\[
A \approx 63.375 \times 3.14159 \approx 199.0 \text{ in}^2
\]

Rounding, we have:

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

Thus, the area of the sector is approximately:

**A = 199.1 in.²**