follow the steps to find the area of the shaded region. first, use the formula below to find the area of the…

follow the steps to find the area of the shaded region. first, use the formula below to find the area of the whole sector. sector area = (\\frac{angle of sector}{360})\\pi r^{2} sector area = ? cm^{2} round to four decimal places.

follow the steps to find the area of the shaded region. first, use the formula below to find the area of the whole sector. sector area = (\\frac{angle of sector}{360})\\pi r^{2} sector area = ? cm^{2} round to four decimal places.

Answer

Explanation:

Step1: Identify values

The radius $r = 8$ cm and the angle of the sector $\theta=129^{\circ}$.

Step2: Substitute into formula

The formula for the area of a sector is $A=\left(\frac{\theta}{360}\right)\pi r^{2}$. Substitute $\theta = 129$, $r = 8$ into it: $A=\left(\frac{129}{360}\right)\pi\times8^{2}$.

Step3: Calculate

First, $8^{2}=64$. Then $\frac{129}{360}\times64\pi=\frac{129\times64\pi}{360}=\frac{8256\pi}{360}=\frac{688\pi}{30}=\frac{344\pi}{15}\approx 72.0353$ (rounded to four - decimal places).

Answer:

$72.0353$