the measure of central angle rst is π radians. what is the area of the shaded sector? 4π units² 8π units²…

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{1}{2}r^{2}\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians.

Step2: Identify the radius and central - angle values

From the problem, the radius of the circle $r = 4$ and the central angle $\theta=\pi$ radians.

Step3: Substitute values into the formula

Substitute $r = 4$ and $\theta=\pi$ into the formula $A=\frac{1}{2}r^{2}\theta$. We get $A=\frac{1}{2}\times4^{2}\times\pi$. First, calculate $4^{2}=16$. Then, $\frac{1}{2}\times16\times\pi = 8\pi$.

Answer:

$8\pi$ units$^{2}$