1. 11.6 –Areas of Regular Polygons

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

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 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 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 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 17.1°

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

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

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

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

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

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

16. 4. Find the area of the polygon. 4 2 = a 2 + 2 2 16 = a 2 + 4 12 = a 2 Apothem = _____________ A = ____________________

17. 5. Find the area of the polygon. c 2 = a 2 + b 2 6.8 2 = a 2 + 4 2 30.24 = a 2 5.5 = a 5.5 Apothem = _____________ A = ____________________ 5.5in 46.24 = a 2 + 16

18. m  ACB = _______ 12cm 120° 60° 24cm Apothem = ___________ A = __________________ 6. Find the area of the polygon. 30°

19. 6. Find the area of the polygon. 30°60°90° 1  2 12cm m  ACB = _______ 120° Apothem = ___________ A = __________________ 30°

20. 6. Find the area of the polygon. 12cm m  ACB = _______ 120° Apothem = ___________ A = __________________

21. 60° 30° 5m 7. Find the area of the polygon. 5m m  ACB = _______ 60° Apothem = ___________ A = __________________ 60°

22. 7. Find the area of the polygon. 30°60°90° 1 2 30° 5m m  ACB = _______ 60° Apothem = ___________ A = __________________ 60°

23. 7. Find the area of the polygon. 30° 5m m  ACB = _______ 60° Apothem = ___________ A = __________________

24. 72° 36° 8. Find the area of the polygon. m  ACB = _______ 72° Side Length = ________ A = __________________

25. 36° SOH – CAH – TOA 1 = x15.98 O A H 8. Find the area of the polygon. m  ACB = _______ 72° Side Length = ________ A = __________________ 31.96cm

26. 36° 15.98 O A H 8.Find the area of the polygon. m  ACB = _______ 72° Side Length = ________ A = __________________ 31.96cm

27. 45° 22.5° 9. Find the area of the polygon. m  ACB = __________ Apothem = __________ Side Length = ________ A = __________________

28. 22.5° SOH – CAH – TOA 1 = a5.54 O A H 1 = x2.3 9. Find the area of the polygon. m  ACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in 2.3

29. 22.5° 5.54 O A H 2.3 9. Find the area of the polygon. m  ACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in