### Home > MC2 > Chapter 6 > Lesson 6.2.3 > Problem6-101

6-101.

Find the area of each shaded sector (region) in the circles below. Note that the smaller angles in parts (a) and (c) are $90°$ angles.

1. A circle has a total measure of $360°$. To find the area of the shaded sector, you must find the fraction of the circle that is shaded.

If the smaller angle of the non-shaded area is $90°$, the shaded portion's angle must be $270°$.
$270°$ as a portion of
$360°= \frac{270°}{360°}=\frac{3}{4}$

This portion represents the fraction of the area that the shaded sector represents in the circle.
The area of a circle is $π(r^2)$.
Substituting in $9$ ft for the radius, we get about $254.4$ ft$^{2}$ for the total area of the circle.

$\frac{3}{4}$ of $254.4$ ft$^2$$=$ about $190.8$ ft$^2$

b.

See part (a).

1. $176.6$ ft$^{2}$