8.4 areas of regular polygons
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8.4 Areas of Regular Polygons. Area of Regular Polygons. A regular polygon has equal sides and equal angles The radius of the polygon is the distance from the center to a vertex. radius. center. Area of Regular Polygons. - PowerPoint PPT PresentationTRANSCRIPT
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8.4 Areas of Regular Polygons
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Area of Regular Polygons
A regular polygon has equal sides and equal angles
The radius of the polygon is the distance from the center to a vertex
center
radius
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Area of Regular Polygons
Drawing all of the radii will create several congruent, isosceles triangles.
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Area of Regular Polygons
The apothem is the perpendicular distance from the center to the midpoint of one of the sides.
center
apothem
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Area of Regular Polygons
An apothem bisects one of the angles created by two radii, creating another pair of congruent triangles
apothem
radii
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Area of Regular Polygons
Example: Find the measure of each numbered angle
3
2
1
m∠1=
m∠2=
m∠3=
360∕6 = 60°
60∕2 = 30°
180-90-30=60°
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Area of Regular Polygons
Example: Find the measure of each numbered angle
65 4
m∠4=
m∠5=
m∠6=
360∕8 = 45°
45∕2 = 22.5°
180-90-22.5=67.5°
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Area of Regular Polygons
Example: Find the measure of each numbered angle
9
8
7
m∠7=
m∠8=
m∠9=
360∕5= 72°
72∕2 = 36°
180-90-36=54°
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Area of Regular Polygons
The area of a regular polygon equals one half the product of the apothem and the perimeter
or
Perimeter equals the side length times the number of sides: p =
s*n
paA 2
1
A= ½ a*s*n
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Area of Regular Polygons
Example: Find the area of the regular polygon
8 in
12.3 in
paA 2
1
803.122
1A
2in 492A
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Area of Regular Polygons
Example: Find the area of the regular polygon
18 ft23.5 ft
9 ft
21.7 ft
paA 2
1
1447.212
1A
2ft 4.1662A
Use Pythagorean Theorem!
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Area of Regular Polygons
Example: Find the area of the regular polygon
7.2
6.1
3.6
4.9
paA 2
1
1447.212
1A
2ft 4.1662A
Use Pythagorean Theorem!
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Area of Regular Polygons
Example: Find the area of the regular polygon
10 cm
60
30
5
5√3 10
Use shortcut for 30-60-90 triangle!
2cm 1.259860352
1A
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Area of Regular Polygons
Example: Find the area of the regular polygon
60
307.8
4.515.6 m
Use shortcut for 30-60-90 triangle!
2m 32.112
8.468.42
1
A
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Area of Regular Polygons
Homework – 8.4/1-8,13-15,20-21Due: Tomorrow