area of regular polygons 11.2 chapter 11 areas of polygons and circles section 11.2 area of regular...
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![Page 1: Area of Regular Polygons 11.2 Chapter 11 Areas of Polygons and Circles Section 11.2 Area of Regular Polygons Find the area of an equilateral triangle](https://reader036.vdocuments.net/reader036/viewer/2022081504/5697bfc41a28abf838ca61d3/html5/thumbnails/1.jpg)
Area of Regular Polygons11.2
Chapter 11Areas of Polygons and Circles
Section 11.2
Area of Regular Polygons
Find the area of an equilateral triangle
Find the area of a regular polygon
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Area of Regular Polygons11.2
Example 1 Area Equilateral Triangle
Example 2 Area Regular Pentagon
Example 3 Area Regular Octagon
Example 4 Always, Sometimes, Or Never
CA Standard 12.0
Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Key)
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Area of Regular Polygons11.2
Find the area of an equilateral triangle
12
A bh
60° 60°
30°
2s
2s
32s
1 32 2
sA s
2 34
sA
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Area of Regular Polygons11.2
Find the area of an equilateral triangle
2 34
sA
25 34
25 34
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Area of Regular Polygons11.2
Find the area of an equilateral triangle
Find the area of the triangle
The Triangle is equilateral with s = 11
2 34
sA Area Equilateral
211 34
A s = 11
121 34
A Simplify
Answer: The triangle has area of square units121 3
52.44
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Area of Regular Polygons11.2
Find the area of an equilateral triangle
Find the area of the triangle
Answer: The triangle has area of square units5 3
2.24
5 5
5
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Area of Regular Polygons11.2
Center of circumscribed circle
Radius of circumscribed circle
Distance from center to any side of the polygons
Vertex is on the center, Sides connect consecutive vertices
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Area of Regular Polygons11.2
To find the area of the hexagon, find the area of one triangle and multiply by 6
12
6 bhA
Height of the triangle is an apothem of the hexagon
Base of the triangle is a side of the hexagon
6 is the number of sides of the hexagon
12ans
b
h
12
n as
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Area of Regular Polygons11.2
Find the area of a regular polygon
5
4
Perimeter = ns = 5(5) = 25 units
1 1(4)(5)(5) 50
2 2Area ans square units
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Area of Regular Polygons11.2
Find the area of a regular polygon
Need to find the apothem and side length
Apothem = BD
Side Length = AC
Look at ABC
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Area of Regular Polygons11.2
1(360) 72
5m ABC
Find the area of a regular polygon
1(72) 36
2m DBC
Find BD and AC
BD = cos 36 AC = 2 sin 36
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Area of Regular Polygons11.2
Find the area of a regular polygon
Apothem = BD = cos 36
s = AC = 2(DC) = 2 sin 36
12
A ans
1(cos36)(5)(2sin36)
2A
5(cos36)(sin36)A
2.4A square units
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Area of Regular Polygons11.2
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
Need to find the apothem and side length
a
s
Central Angle has measure 360 8 = 45
This angle is half the
Central Angle
45 2 = 22.5
This length is half of s
2s
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Area of Regular Polygons11.2
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
Need to find a and s using the triangle
cos 22.53a 3cos 22.5a
2sin 22.53
s
3sin 22.52s
s = 6 sin 22.5
a
2s
22.5°
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Area of Regular Polygons11.2
Find the area of a regular polygon
Find the area of an octagon with radius 3 cm
a
s
2s
12
A ans
1(3cos22.5)(8)(6sin 22.5)
2
225.5cm
3cos 22.5a s = 6 sin 22.5
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Area of Regular Polygons11.2
Find the Area and Perimeter of the following pentagon
Find the measures of interior and exterior angles of polygons
Answer: Area = 1125 tan 36 817.4 Square UnitsPerimeter = 150 tan 36 109 Units
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Area of Regular Polygons11.2
Always
Always
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Area of Regular Polygons11.2
HW # 48Pg 672-675 9-29, 30-52