Question

the measure of central angle rst is π radians. what is the area of the shaded sector? 4π units² 8π units² 16π units² 20π units²

Explanation:

Step1: Recall the 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 values of $r$ and $\theta$

From the figure, the radius $r = 4$ units and the central - angle $\theta=\pi$ radians.

Step3: Substitute the values into the formula

$A=\frac{1}{2}\times4^{2}\times\pi$.
First, calculate $4^{2}=16$. Then, $\frac{1}{2}\times16\times\pi = 8\pi$ square units.

Answer:

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