1. Area of a Circle
Recall that when investigating the area of certain polygons, we based our new area formulas on shapes whose area we already knew. We’ll do the same with the area of a circle.

2. Area of a Circle
Recall that when investigating the area of certain polygons, we based our new area formulas on shapes whose area we already knew. We’ll do the same with the area of a circle.

3. Area of a Circle
Recall that when investigating the area of certain polygons, we based our new area formulas on shapes whose area we already knew. We’ll do the same with the area of a circle.

4. Area of a Circle

5. Area of a Circle Theorem
The area of a circle is π times the square of the radius.

6. Sector: An Actual Slice of Pie
A sector of a circle is the region between two radii of a circle and the included arc.

7. Got any vanilla ice cream for that?
Example 14
Remember that delicious cherry pie from Example 5? Well, it’s mostly a memory now, as there is only one slice left! What is the area of that piece of pie if the radius is 6 inches and the angle formed by the sides of the pie slice is 60°?
Got any vanilla ice cream for that?

8. Area of a Sector Conjecture
If the radius of a circle is r and two radii form a central angle of a°, then the area of the sector formed by those radii is given by the formula

9. Area of a Sector Conjecture
If the radius of a circle is r and two radii form a central angle of a°, then the area of the sector formed by those radii is given by the formula

10. Example 15
The radius of a circle is 18 cm. A sector is formed by a central angle measuring 40°. What is the exact area of the sector?

11. Example 16
Find the area of each sector.

12. Example 17
Find the area of circle S.
Find the radius of circle S.

13. Example 18
What is the area of the shaded region if the radius of each circle is 6 cm.

14. Segment of a circle

15. Example
Find the area of the following segments

16. Example
Find the area of the following segments