CHAPTER 10 / ESSENTIAL GEOMETRY SKILLS 383
the horizontal part of the “simple” path along the
rectangle. The same is true of the vertical parts. So
the perimeter is 15 + 20 + 15 + 20 =70.Example:
If the circle with center Chas an area of 16π, what
is the area of the shaded region?
Piece together the strange shape from simple shapes.
Notice that the shaded region is simply a quarter of
the circle minus the triangle. If the area of the circle
is 16π, then a quarter of the circle has an area of 4π.
Since πr^2 = 16 π, the radius must be 4. Therefore, the
base and height of the triangle are both 4, and the
area of the triangle is (4×4)/2 =8. Therefore, the area
of the shaded region is 4π−8.