Question

Can you please help me

Answer 1

To obtain the area of the shaded sector, the following steps are necessary:

Step 1: Recall the formula for the area of a sector, as below:

`A_(\sec tor)=(\theta)/(360)*\pi* r^2`

Where:

`\begin{gathered} \theta=\sec tor\text{ angle} \\ r=\text{radius of circle} \\ \pi=3.142.. \end{gathered}`

Step 2: Apply the formula to obtain the area of the shaded sector in the question, as follows:

`\begin{gathered} A_(\sec tor)=(\theta)/(360)*\pi* r^2 \\ \sin ce\colon\text{ }\theta=36^o,\text{ and r= 6 in, we have:} \\ A_(\sec tor)=(36)/(360)*\pi*6^2 \\ \Rightarrow A_(\sec tor)=(36)/(360)*3.142*36 \\ \Rightarrow A_(\sec tor)=(4072.032)/(360)=11.31in^2 \\ \Rightarrow A_(\sec tor)=11.31in^2 \end{gathered}`

Therefore, the area of the shaded sector is 11.31 square inches (option B)