Areas of Polygonal Regions
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Areas of Polygonal Regions
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1. Areas of Triangular Regions
Theory
Page 10
The Concept of Area
Theory
Page 10
Basic Definitions
Theory
Page 10
Area of a Rectangle
Theory
Page 11
Area of a Triangle
Theory
Page 14
Theorem: Base-Height Formula
Theory
Page 14
Theorem: Area of a Right Triangle
Theory
Page 17
Theorem: Area of an Equilateral Triangle
Theory
Page 19
Theorem: Heron's Formula
Theory
Page 21
Theorem: Trigonometric Formula for the Area of a Triangle
Theory
Page 22
Theorem: Area of a Triangle by Its Inradius
Theory
Page 24
Theorem: Area of a Triangle by Its Circumradius
Theory
Page 26
Properties of the Area of a Triangle
Theory
Page 27
Pick's Theorem
Theory
Page 44
Exercises 1
Problem
Page 46
2. Areas of Quadrilaterals
Theory
Page 51
Area of a Quadrilateral
Theory
Page 51
Theorem: Area of a Convex Polygon
Theory
Page 52
Area of a Parallelogram
Theory
Page 56
Theorem: Area of a Parallelogram
Theory
Page 56
Area of a Rhombus
Theory
Page 63
Area of a Square
Theory
Page 66
Area of a Trapezoid
Theory
Page 69
Theorem: Area of a Trapezoid
Theory
Page 69
Area of a Kite
Theory
Page 79
Proving the Pythagorean Theorem
Theory
Page 81
Exercises 2
Problem
Page 83
3. Areas of Regular Polygons and Circles
Theory
Page 89
Area of a Regular Polygon
Theory
Page 89
Theorem: Area of a Regular Polygon
Theory
Page 90
Area of a Circular Region
Theory
Page 93
Theorem: Area of a Circle
Theory
Page 93
Area of a Sector
Theory
Page 97
Theorem: Area of a Sector
Theory
Page 97
Area of a Segment
Theory
Page 102
Theorem: Area of a Segment
Theory
Page 102
Area of a Ring
Theory
Page 105
Ratios in Circles
Theory
Page 107
Three Unsolved Problems
Problem
Page 110
Exercises 3
Problem
Page 112
Chapter Summary
Other
Page 116
Concept Check
Test
Page 121
Chapter Review Test 1
Test
Page 123
Chapter Review Test 2
Test
Page 125
Chapter Review Test 3
Test
Page 127
Chapter Review Test 4
Test
Page 129
Answers
Answer
Page 131
Glossary
Other
Page 133
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