find the area of the smaller sector.
round to the nearest tenth.
area = ? in²

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the area of a sector
The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central angle of the sector and $r$ is the radius of the circle.
## Step2: Identify the values of $\theta$ and $r$
Given $\theta = 77^{\circ}$ and $r = 10.7$ in.
## Step3: Substitute the values into the formula
$$
\begin{align*}
A&=\frac{77}{360}\times\pi\times(10.7)^{2}\
&=\frac{77}{360}\times\pi\times114.49\
\end{align*}
$$
## Step4: Calculate the value
$$
\begin{align*}
A&=\frac{77\times114.49\times\pi}{360}\
&=\frac{8815.73\times\pi}{360}\
&\approx\frac{8815.73\times3.1416}{360}\
&=\frac{27790.1}{360}\
&\approx77.2
\end{align*}
$$

# Answer:
$77.2$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Identify the values of \(\theta\) and \(r\)

Step3: Substitute the values into the formula

Step4: Calculate the value

Answer: