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11.6 –Areas of Regular Polygons
Center of a polygon:
Point equidistant to the vertices of the polygon
center
Radius of a polygon:
Length from the center to the vertex of a polygon
PM
PN
Apothem of the polygon:
Length from the center to the side of a polygon
PQ
Central angle of a regular polygon:
Angle formed by two radii in a polygon
MPN∠
360
n
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 =
360
n=
360
6= 60°
60°
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 =
360
n=
360
12= 30°
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 =
360
n=
360
40= 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 =
360
n=
360
21≈ 17.1°
2. Find the given angle measure for the regular hexagon shown.
Each central angle =
360
n=
360
6= 60°
2. Find the given angle measure for the regular hexagon shown.
m∠EGF = 60°
60°
2. Find the given angle measure for the regular hexagon shown.
m∠EGD = 60°
60°
2. Find the given angle measure for the regular hexagon shown.
m∠EGH = 30°
60°30°
2. Find the given angle measure for the regular hexagon shown.
m∠DGH = 30°
60°30°30°
2. Find the given angle measure for the regular hexagon shown.
m∠GHD = 90°
1
2A san=
Area of a regular polygon:
s = side length
a = apothem length
n = number of sides
3. A regular pentagon has a side length of 8in and an apothem length of 5.5in. Find the area.
1
2A san=
1(8)(5.5)(5)
2A =
(4)(27.5)A =
2110A in=
4. Find the area of the polygon.
Central Angle = _______
Central Angle =
360
n=
360
6= 60°
60°
4. Find the area of the polygon.
c2 = a2 + b2
42 = a2 + 22
16 = a2 + 412 = a2
2 3 a=
2 3
1
2A san=
1(4)(2 3)(6)
2A =
(2)(12 3)A =
224 3A in=
Apothem = __________ 2 3in
5. Find the area of the polygon.
Central Angle = _______
Central Angle =
360
n=
360
5= 72°
72°
5. Find the area of the polygon.
c2 = a2 + b2
6.82 = a2 + 42
46.24 = a2 + 1630.24 = a2
1
2A san=
1(8)(5.5)(5)
2A =
A =110in2
5.5 = a
5.5
Apothem = __________ 5.5in
6. Find the area of the polygon.
m∠ACB = _______ 12cm 12cm
Central Angle =
360
n=
360
3= 120°
120°
60°60°
24cm
30°
6. Find the area of the polygon.
30° 60° 90°
1 3
12
3a =
3 12a =
a 12 b
=3
3
12 3
3=
2
12cm 12cm
4 3
4 3
Apothem = __________ 4 3cm
30°
1
2A san=
1(24)(4 3)(3)
2A =
2144 3A cm=
6. Find the area of the polygon.
4 3
12cm 12cm
30°
m∠ACB = _______
Central Angle =
360
n=
360
6= 60°
60°
30°
5m
7. Find the area of the polygon.
5m60°
7. Find the area of the polygon.
30° 60° 90°
1 3
5 3a =
5 a b
230°
5m5m
5 3
Apothem = __________ 5 3m
60°
1
2A san=
1(10)(5 3)(6)
2A =
A =150 3m2
7. Find the area of the polygon.
30°
5m5m
5 3
8. Find the area of the polygon.
m∠ACB = _______
Central Angle =
360
n=
360
5=72°
72°
36°
8. Find the area of the polygon.
36°
SOH – CAH – TOA
tan 3622
x° =
1
22 tan 36 x° =
= x 15.98
15.9815.98Side Length = __________31.96 cm
8. Find the area of the polygon. Round to two decimal places.
36°
15.9815.98
1
2A san=
A =
12(31.96)(22)(5)
A =1757.8cm2
m∠ACB = _______
Central Angle =
360
n=
360
8=45°
45°
22.5°
9. Find the area of the polygon. Round to two decimal places.
22.5°
SOH – CAH – TOA
cos 22.56
a° =
1
6cos 22.5 a° =
= a 5.54 5.54
9. Find the area of the polygon. Round to two decimal places.
apothem = _______5.54 in
22.5°
SOH – CAH – TOA
sin 22.56
x° =
1
6sin 22.5 x° =
= x 2.3 5.54
2.32.3
9. Find the area of the polygon. Round to two decimal places.
Side length = _______4.6 in
22.5°
5.54
2.3
1
2A san=
1(4.6)(5.54)(8)
2A =
2101.94A in=2.3
9. Find the area of the polygon. Round to two decimal places.