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°
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. 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°
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°
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.
Apothem = _____________
A = ____________________

17. 5. Find the area of the polygon.
c2 = a2 + b2
6.82 = a2 + 42
46.24 = a2 + 16
30.24 = a2
5.5
5.5 = a
5.5in
Apothem = _____________
A = ____________________

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

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

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

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

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

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

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

25. H A O 8. Find the area of the polygon. SOH – CAH – TOA 1 15.98 = x
36° H A
15.98
= x
15.98
15.98 O
mACB = _______
72°
31.96cm
Side Length = ________
A = __________________

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

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

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

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

30. HW Problems
11.6
1-4, 8-11, 14-16, 19-21
#20 H
36° O
2.98 A
2.98
SOH – CAH – TOA
29.8u
2.98
= x