"Published in Newark, California, USA"
Find the area of the shaded region:
 |
| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
|
| Photo by Math Principles in Everyday Life |
The first thing that we need to do is to label further the given figure so that we can solve for the area of circular segment which is the unshaded portion as follows
 |
| Photo by Math Principles in Everyday Life |
The angle of an arc is equal to the angle of circular sector which is 120°. If you draw a line which is perpendicular to the given chord, then it becomes two equal right triangles and that line will bisect the angle of circular sector. In this case, there are two 30° - 60° right triangles. Hence, the area of circular segment is
where θ is the angle of circular section in radians (a unit less value of angle). Substitute the values, we have
The area of a circle is
Therefore, the area of shaded region is
