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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 Presentation
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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
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)
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
Area of Regular Polygons11.2
Find the area of an equilateral triangle
2 34
sA
25 34
25 34
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
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
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
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
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
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
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
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
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
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°
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
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
Area of Regular Polygons11.2
Always
Always
Area of Regular Polygons11.2
HW # 48Pg 672-675 9-29, 30-52
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