1. Lesson 11-6 Arc Lengths and Areas of Sectors (page 452) Essential Question How can you calculate the area of any figure?

2. Arc Lengths & Areas of Sectors

3. Two different numbers that describe the size of an arc are: A O B (1)the measure of the arc, ie.. (2)the arc length, which is the length of a piece of the circumference.

4. The arc length is a fraction of the whole circumference. The length of the arc equals the fraction times the circumference of the circle. A O B xº

5. A sector of a circle is a region bounded by two radii and an arc of the circle. The area of a sector is a fraction of the area of the whole circle. A O B xº

6. Area of a Sector The area of a sector equals the fraction times the area of the circle. A O B xº

7. #1 In O with radius 6 and m ∠ AOB = 150º, find the lengths of and. A O B D C 10º 150º r = 6

8. #1 In O with radius 6 and m ∠ AOB = 150º, find the lengths of and. A O B D C 10º 150º r = 6 200º

9. #2 Find the area of the shaded sector in the circle with radius equal to 12. 40º r = 12

10. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º Please note: This is also referred to as the Area of a Segment.

11. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º WARNING? We do not have a formula for this figure!

12. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º

13. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º General approach: A shaded region = A big region - A small region For this problem: A shaded region = A sector - A triangle

14. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º A shaded region = A sector - A triangle r = 6

15. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

16. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

17. #3 Find the area of the shaded region in the circle with radius equal to 6. 120º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

18. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º WARNING? We do not have a formula for this figure!

19. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º

20. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º General approach: A shaded region = A region + A region For this problem: A shaded region = A sector + A triangle

21. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º A shaded region = A sector + A triangle r = 2”

22. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 2”2” A shaded region = A sector + A triangle 60º

23. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 30º 60º A shaded region = A sector + A triangle 2”2”

24. #4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 30º 60º A shaded region = A sector + A triangle 2”2”

25. Chapter 11 Project Assignment Circle Graph Activity This is due _________________! Please make this VERY nice! How can you calculate the area of any figure?

26. Assignment Written Exercises on pages 453 & 454 REQUIRED: 1 to 19 odd numbers How can you calculate the area of any figure? UPDATE YOUR STUDENT AID CARD!