chapter 11 areas of polygons and circles
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Find the area of a regular polygon. Find the area of an equilateral triangle. Chapter 11 Areas of Polygons and Circles. Section 11.2 Area of Regular Polygons. Lesson 1 Contents. Example 1 Area Equilateral Triangle Example 2 Area Regular Pentagon Example 3 Area Regular Octagon - PowerPoint PPT PresentationTRANSCRIPT
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Area of Regular Polygons11.2
Chapter 11Areas of Polygons and Circles
Section 11.2Area 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
sA25 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 = 112 34
sA Area Equilateral
211 34
A s = 11
121 34
A Simplify
Answer: The triangle has area of square units121 3 52.4
4
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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 2.2
4
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 hexagonBase of the triangle is a side of the hexagon
6 is the number of sides of the hexagon
12ans
b
h12
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) 502 2
Area 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) 725
m ABC
Find the area of a regular polygon
1 (72) 362
m 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)2
A
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
cos22.53a 3cos22.5a
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