Answer:
[tex]9\pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The measure of central angle ABC is [tex]\frac{\pi}{2}[/tex] radians
so
[tex]\frac{\pi}{2}=90\°[/tex]
[tex]360\°[/tex] subtends the complete circle
The area of the shaded sector is the area of a quarter circle
so
The area of a quarter circle is equal to
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=6\ units[/tex]
substitute
[tex]A=\frac{1}{4}\pi (6)^{2}=9\pi\ units^{2}[/tex]
