Embed Size (px)
DESCRIPTION
11.6 –Areas of Regular Polygons. Center of a polygon:. Point equidistant to the vertices of the of the polygon. P. Radius of a polygon:. Length from the center to the vertex of a polygon. Apothem of the polygon:. Length from the center to the side of a polygon. - PowerPoint PPT Presentation
Citation preview
11.6 –Areas of Regular Polygons
Center of a polygon:
Point equidistant to the vertices of the of the polygon
P
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
MPN360
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
360
n360
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
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
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
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°
mEGF = 60°
60°
mEGD = 60°
2. Find the given angle measure for the regular hexagon shown.
mEGH = 30°
60°30°
2. Find the given angle measure for the regular hexagon shown.
mDGH = 30°
60°30°30°
2. Find the given angle measure for the regular hexagon shown.
mGHD = 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.
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 = _____________
A = ____________________
2 3in224 3in
5. Find the area of the polygon.
c2 = a2 + b2
6.82 = a2 + 42
30.24 = a2
1
2A san
1(8)(5.5)(5)
2A
(4)(27.5)A
2110A in
5.5 = a
5.5
Apothem = _____________
A = ____________________2110in
5.5in
46.24 = a2 + 16
mACB = _______
12cm 12cm
360
n
360
3120°
120°
60°60°
24cm
Apothem = ___________
A = __________________
6. Find the area of the polygon.
30°
6. Find the area of the polygon.
30° 60° 90°
1 3
12
3a
3 12a
a 12 H
3
3
12 3
3
2
12cm 12cm
4 3
4 3
mACB = _______120°
Apothem = ___________
A = __________________
30°
4 3cm
1
2A san
1(24)(4 3)(3)
2A
(12)(12 3)A
2144 3A cm
6. Find the area of the polygon.
4 3
12cm 12cm
mACB = _______120°
Apothem = ___________
A = __________________
4 3cm
2144 3cm
360
n
360
6 60°
30°
5m
7. Find the area of the polygon.
5m
mACB = _______60°
Apothem = ___________
A = __________________
60°
7. Find the area of the polygon.
30° 60° 90°
1 3
5 3a
5 a H
230°
5m5m
5 3
5 3mmACB = _______60°
Apothem = ___________
A = __________________
60°
1
2A san
1(10)(5 3)(6)
2A
(5)(30 3)A
A 150 3m2
7. Find the area of the polygon.
30°
5m5m
5 3
5 3mmACB = _______60°
Apothem = ___________
A = __________________ 150 3m2
360
n
360
5 72°
36°
8. Find the area of the polygon.
mACB = _______72°
Side Length = ________
A = __________________
36°
SOH – CAH – TOA
tan 3622
x
1
22 tan 36 x
= x 15.98 15.9815.98O
AH
8. Find the area of the polygon.
mACB = _______72°
Side Length = ________
A = __________________
31.96cm
1
2A san
1(31.96)(22)(5)
2A
21757.8A cm
36°
15.9815.98O
AH
8. Find the area of the polygon.
mACB = _______72°
Side Length = ________
A = __________________
31.96cm
21757.8cm
360
n
360
8 45°
45°
22.5°
9. Find the area of the polygon.
mACB = __________
Apothem = __________
Side Length = ________
A = __________________
22.5°
SOH – CAH – TOA
cos 22.56
a
1
6cos 22.5 a
= a 5.545.54
O
AH
sin 22.56
x
1
6sin 22.5 x
= x 2.3
9. Find the area of the polygon.
mACB = __________
Apothem = __________
Side Length = ________
A = __________________
45°5.54in
4.6in
2.3 2.3
1
2A san
1(4.6)(5.54)(8)
2A
2101.94A in
22.5°
5.54
O
AH
2.3 2.3
9. Find the area of the polygon.
mACB = __________
Apothem = __________
Side Length = ________
A = __________________
45°5.54in
4.6in2101.94in
11.6 765-767 1-4, 8-11, 14-16, 19-21
HW Problems
#20
1
2A san
36°
SOH – CAH – TOA
tan 364.1
x
= x 2.98
OA
H2.98
2.98 15.96 4.1 5
2A
261.09A u
5 5.96P 29.8u
