find the area of the shaded sector of the circle. the area of the shaded sector is m². (simplify your…

Explanation:

Step1: Recall area - of - circle formula

The area of a full - circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, $r = 26$ m, so $A=\pi\times(26)^{2}=676\pi$ $m^{2}$.

Step2: Find the fraction of the circle

The measure of the central angle of the sector is $\theta = 150^{\circ}$, and the measure of a full - circle is $360^{\circ}$. The fraction of the circle that the sector represents is $\frac{\theta}{360}=\frac{150}{360}=\frac{5}{12}$.

Step3: Calculate the area of the sector

The area of the sector $A_{s}$ is the fraction of the circle times the area of the full - circle. So $A_{s}=\frac{5}{12}\times676\pi=\frac{3380\pi}{12}=\frac{845\pi}{3}$ $m^{2}$.

Answer:

$\frac{845\pi}{3}$