the measure of central angle xyz is 1.25π radians. what is the area of the shaded sector? 10π units² 20π…

Answer:

40π 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 given values

We are given that $r = 8$ and $\theta=1.25\pi$ radians.

Step3: Substitute values into formula

$A=\frac{1}{2}(8)^{2}(1.25\pi)$. First, calculate $(8)^{2}=64$. Then, $\frac{1}{2}\times64 = 32$. Now, $A = 32\times1.25\pi$. Since $1.25=\frac{5}{4}$, then $32\times\frac{5}{4}\pi$. $32\times\frac{5}{4}=40$. So, $A = 40\pi$ units².