1. 11.6 –Areas of Regular Polygons

2. Center of a polygon: Point equidistant to the vertices of the polygon center

3. Radius of a polygon: Length from the center to the vertex of a polygon

4. Apothem of the polygon: Length from the center to the side of a polygon

5. Central angle of a regular polygon: Angle formed by two radii in a polygon

6. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 6 sides Central Angle = 60°

7. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 12 sides Central Angle = 30°

8. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 40 sides Central Angle = 9°9°

9. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 21 sides Central Angle = 17.1°

10. 2. Find the given angle measure for the regular hexagon shown. Each central angle = 60°

11. 2. Find the given angle measure for the regular hexagon shown. m  EGF = 60°

12. 2. Find the given angle measure for the regular hexagon shown. m  EGD = 60°

13. 2. Find the given angle measure for the regular hexagon shown. m  EGH = 30° 60° 30°

14. 2. Find the given angle measure for the regular hexagon shown. m  DGH = 30° 60° 30°

15. 2. Find the given angle measure for the regular hexagon shown. m  GHD = 90°

16. Area of a regular polygon: s = side length a = apothem length n = number of sides

17. 3. A regular pentagon has a side length of 8in and an apothem length of 5.5in. Find the area.

18. 4. Find the area of the polygon. Central Angle = _______ Central Angle = 60°

19. 4. Find the area of the polygon. c 2 = a 2 + b 2 4 2 = a 2 + 2 2 16 = a 2 + 4 12 = a 2 Apothem = __________

20. 5. Find the area of the polygon. Central Angle = _______ Central Angle = 72°

21. 5. Find the area of the polygon. c 2 = a 2 + b 2 6.8 2 = a 2 + 4 2 46.24 = a 2 + 16 30.24 = a 2 5.5 = a 5.5 Apothem = __________

22. 6. Find the area of the polygon. m  ACB = _______ 12cm Central Angle = 120° 60° 24cm 30°

23. 6. Find the area of the polygon. 30°60°90° 1  2 12cm Apothem = __________ 30°

24. 6. Find the area of the polygon. 12cm 30°

25. m  ACB = _______ Central Angle = 60° 30° 5m 7. Find the area of the polygon. 5m 60°

26. 7. Find the area of the polygon. 30°60°90° 1 2 30° 5m Apothem = __________ 60°

27. 7. Find the area of the polygon. 30° 5m

28. 8. Find the area of the polygon. m  ACB = _______ Central Angle = 72° 36°

29. 8. Find the area of the polygon. 36° SOH – CAH – TOA 1 = x15.98 Side Length = __________ 31.96 cm

30. 8. Find the area of the polygon. Round to two decimal places. 36° 15.98

31. m  ACB = _______ Central Angle = 45° 22.5° 9. Find the area of the polygon. Round to two decimal places.

32. 22.5° SOH – CAH – TOA 1 = a5.54 9. Find the area of the polygon. Round to two decimal places. apothem = _______ 5.54 in

33. 22.5° SOH – CAH – TOA 1 = x2.3 5.54 2.3 9. Find the area of the polygon. Round to two decimal places. Side length = _______ 4.6 in

34. 22.5° 5.54 2.3 9. Find the area of the polygon. Round to two decimal places.