1. 7.7 Areas of Circles and Sectors

2. Quick Review What is the circumference of a circle? What is the area of a circle? The interior angle sum of a circle is ? What is the arc length formula?

3. Sector of a Circle Formula is very similar to arc length Notation is slightly different! - The center pt is used when describing a sector. - The is not used for sectors.

4. How can we find area, based on what we already know?

6. Area of a sector =

7. 1. Find the area of the shaded sector 2. Find the arc length of the shaded sector.

8. Segment any ideas of how to find the shaded area?

9. Finding the Area of a Segment of a Circle –= Area of Sector Area of Triangle Area of Segment minusequals

10. Find the area of segment RST to the nearest hundredth. Use formula for area of sector. Substitute 4 for r and 90 for m. = 4 π m 2 Step 1 Find the area of sector RST.

11. Simplify. Step 2 Find the area of ∆ RST. Continued Find the area of segment RST to the nearest hundredth. ST = 4 m, and RS = 4m. = 8 m 2

12. Step 3 area of segment = area of sector RST – area of ∆ RST  4.57 m 2 Find the area of segment RST to the nearest hundredth. Continued = 4 π – 8

13. A segment of a circle

14. Find the area of segment LNM to the nearest hundredth. Finding the Area of a Segment Use formula for area of sector. Substitute 9 for r and 120 for m. = 27 π cm 2 Step 1 Find the area of sector LNM.

15. Find the area of segment LNM to the nearest hundredth. Continued Step 2 Find the area of ∆ LNM. Draw altitude NO.

16. Find the area of segment LNM to the nearest hundredth. Continued Step 3 area of segment = area of sector LNM – area of ∆ LNM = 49.75 cm 2

17. Find the area of the shaded portion

18. Find the area of the red portion Of the Tube Sign.

19. Find the shaded area with r = 2, 4, & 10

20. 1cm 3cm 5cm What is the Area of the Black part?

21. If you have 2 circles A and B that intersect at 2 points and the distance between the centers is 10. What is the area of the intersecting region? AB 10

22. Classwork Time - Go! Page 397 7 - 27 odd 31-33 36-38