1. Deriving the Formula for the Area of a Sector
Adapted from Walch Education

2. Key Concepts A sector is the portion of a circle bounded
by two radii and their
intercepted arc.
3.4.2: Deriving the Formula for the Area of a Sector

3. Key Concepts, continued
To find the area of a sector, , when the central angle  is given in radians, we can set up a proportion using the area of a circle,
We can solve this proportion for the area of the sector and simplify to get a formula for the area of a sector in terms of the radius of the circle and the radian measure of the central angle .
3.4.2: Deriving the Formula for the Area of a Sector

4. Key Concepts, continued
To find the area of a sector when the central angle is given in degrees, we can set up a proportion using the area of a circle.
3.4.2: Deriving the Formula for the Area of a Sector

5. Practice
A circle has a radius of 24 units. Find the area of a sector with a central angle of 30°.
3.4.2: Deriving the Formula for the Area of a Sector

6. Solution Find the area of the circle. Set up a proportion.
3.4.2: Deriving the Formula for the Area of a Sector

7. Solution, continued
Multiply both sides by the area of the circle to find the area of the sector.
The area of the sector is approximately units2.
3.4.2: Deriving the Formula for the Area of a Sector

8. Your Turn.
A circle has a radius of 6 units. Find the area of a sector with an arc length of 9 units.
3.4.2: Deriving the Formula for the Area of a Sector

9. Thanks for Watching!!!!
Ms. Dambreville