Shaded Regions
To find the area of the shaded region of a figure, subtract the area of the unshaded region from the area of the entire figure.
Example
What is the area of the shaded region formed by the circle and the rectangle in the figure?
A. 15 – 2π
B. 15 – π
C. 14
D. 16 – π
E. 15π
B. 15 – π
C. 14
D. 16 – π
E. 15π
To find the area of the shaded region subtract the area of the circle from the area of the rectangle:
area of rectangle

–

area of circle

3 — 5

–

π — 1^{2}

15

–

π

The answer is (B).
Example
In the figure, the radius of the larger circle is three times that of the smaller circle. If the circles are concentric, what is the ratio of the shaded region’s area to the area of the smaller circle?
A. 10:1
B. 9:1 C. 8:1 D. 3:1 E. 5:2 
Since we are not given the radii of the circles, we can choose any two positive numbers such that one is three times the other.