Question

I need help please it says find the area of each shaded sector. Round to the nearest hundredth place.

Answer 1

Step 1

State the formula for the area of a sector of a circle

$A=\frac{\theta}{360}\times\pi\times r^2$

Step 2

Find the value of θ.

$m\angle WZV=\theta=180-108=72^{o^{}}(sum\text{ of angles on a straight line is }180^o)$

r=wz= 5.3km

Step 3

Find the area of the shaded part.

$\begin{gathered} A=\frac{72}{360}\times\pi\times(5.3)^2 \\ A=\frac{1}{5}\times\pi\times28.09 \\ A=\frac{2809}{500}(\pi)km^2 \end{gathered}$

Since there are 2 of such shaded sectors, they both will have the same area. Therefore the total area of the shaded sectors will be;

$\begin{gathered} \frac{2809}{500}(\pi)km^2\times2 \\ =35.29893506 \\ \approx35.30km^2 \end{gathered}$

Answer; The area of the shaded sector approximately to the nearest hundredth is = 35.30km²