1. Sector Area and Arc Length in Circles
Unit 11: Circles
Sector Area and Arc Length in Circles
Objectives 4/20/12 & 4/23/12
Find the area of sectors.
Find arc lengths.
*Standard 21.0: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

2. Sector Area and Arc Length in Circles
Unit 11: Circles
Sector Area and Arc Length in Circles
Vocabulary
sector of a circle
segment of a circle
arc length
*Standard 21.0: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

3. The area of a sector is a fraction of the circle containing the sector
The area of a sector is a fraction of the circle containing the sector. To find the area of a sector whose central angle measures m°, multiply the area of the
circle by

4. A segment of a circle is a region bounded by an arc and its chord.
Write the degree symbol after m in the formula to help you remember to use degree measure not arc length.
Helpful Hint
A segment of a circle is a region bounded by an arc and its chord.

5. In the same way that the area of a sector is a fraction of the area of the circle, the length of an arc is a fraction of the circumference of the circle.

6. **Examples: Finding the Area of a Sector
1. Find the area of sector HGJ. Give answers in terms of 

7. **Examples: Finding the Area of a Sector
2. Find the area of sector ABC. Give answers in terms of 

8. **Examples: Finding the Area of a Sector
3. Find the area of sector ACB. Give your answer in terms of 

9. **Examples: Finding the Area of a Sector
4. Find the area of sector JKL. Give your answer in terms of 

10. **Examples: Finding the Area of a Segment
5. Find the area of segment LNM and simplify your answer as much as possible.

11. **Examples: Finding the Area of a Segment
6. Find the area of segment RST and simplify your answer as much as possible.

12. **Examples: Finding Arc Length
7. Find the length of Give your answer in terms of  FG

13. **Examples: Finding Arc Length
8. Find the length of Give your answer in terms of  GH

14. **Examples: Finding Arc Length
9. Find the length of an arc with measure 135° in a circle with radius 4 cm. Give your answer in terms of 