Explore the area of sectors of circles by following these steps.
✓ 1. What is the area of circle C?
✓ 2. Move point A to create a central angle of 180°.
The ratio of the central angle measure to the measure of the entire circle is now 1/2.
The area of the sector created by central angle ACB is
the area of the entire circle because the central angle is 1/2 the measure of the entire circle.
✓ 3. Move point A to create a central angle of 90°.
The ratio of the central angle measure to the measure of the entire circle is
.
The area of the sector created by central angle ACB is
the area of the entire circle.
✓ 4. The formula for the area of a sector of a circle is:
#& \frac {\sf \large central \: angle \: measure}{\sf \large whole \: circle \: measure} \times {\sf entire \: area}#&