AREAS OF POLYGONAL REGIONS
CHAPTER 1: AREAS OF TRIANGULAR REGIONS
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1. THE CONCEPT OF AREA
A. Basic Definitions
B. Area of a Rectangle
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2. AREA OF A TRIANGLE
–Theorem: base-height formula
–Theorem: area of a right triangle
–Theorem: area of an equilateral triangle
–Theorem: Heron's Formula
–Theorem: trigonometric formula for the area of a triangle
–Theorem: area of a triangle by its inradius
–Theorem: area of a triangle by its circumradius
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3. PROPERTIES OF THE AREA OF A TRIANGLE
–Pick’s Theorem
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CHAPTER 2: AREAS OF QUADRILATERALS
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1. AREA OF A QUADRILATERAL
–Theorem: area of a convex polygon
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2. AREA OF A PARALLELOGRAM
–Theorem: area of a parallelogram
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3. AREA OF A RHOMBUS
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4. AREA OF A SQUARE
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5. AREA OF A TRAPEZOID
–Theorem: area of a trapezoid
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6. AREA OF A KITE
–Proving the Pythagorean Theorem
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CHAPTER 3: AREAS OF REGULAR POLYGONS AND CIRCLES
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1. AREA OF A REGULAR POLYGON
–Theorem: area of a regular polygon
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2. AREA OF A CIRCULAR REGION
–Theorem: area of a circle
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3. AREA OF A SECTOR
–Theorem: area of a sector
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4. AREA OF A SEGMENT
–Theorem: area of a segment
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5. AREA OF A RING
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6. RATIOS IN CIRCLES
–Three Unsolved Problems