find the area of the blue shaded region.
9.28 cm
68.9°
area = ? cm²
round to the nearest tenth.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the sector
The formula for the area of a sector is $A_{sector}=\frac{\theta}{360}\times\pi r^{2}$, where $\theta = 68.9^{\circ}$ and $r = 9.28$ cm.
$$
\begin{align*}
A_{sector}&=\frac{68.9}{360}\times\pi\times(9.28)^{2}\
&=\frac{68.9}{360}\times\pi\times86.1184\
&\approx\frac{68.9\times3.14\times86.1184}{360}\
\end{align*}
$$
$$
\begin{align*}
A_{sector}&\approx\frac{68.9\times270.411776}{360}\
&\approx\frac{18631.3713664}{360}\
&\approx51.75380935\space cm^{2}
\end{align*}
$$
## Step2: Calculate the area of the triangle
The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}r^{2}\sin\theta$, where $\theta = 68.9^{\circ}$ and $r = 9.28$ cm.
$$
\begin{align*}
A_{triangle}&=\frac{1}{2}\times(9.28)^{2}\times\sin(68.9^{\circ})\
&=\frac{1}{2}\times86.1184\times0.9325\
& = 43.0592\times0.9325\
&\approx40.1627\space cm^{2}
\end{align*}
$$
## Step3: Calculate the area of the shaded region
The area of the shaded region $A = A_{sector}-A_{triangle}$
$$
\begin{align*}
A&=51.75380935 - 40.1627\
&\approx11.6\space cm^{2}
\end{align*}
$$

# Answer:
$11.6\space cm^{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the sector

Step2: Calculate the area of the triangle

Step3: Calculate the area of the shaded region

Answer: