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Polygons

A polygon is a closed-figure in a plane bounded by three or more straight edges

Polygon

 

# of vertices

# of edges

Triangle

Scalene Triangle

Equilateral Triangle

 

 3 3

Quadrilateral

General Quadrilateral

Rectangle

Rhombus

Square

 4 4

Pentagon

5

5

Hexagon

6

6

Heptagon

7

7

Octagon

8

8
Here are some basic theorems and properties governing polygons:

  1. The sum of all interior angles = (n - 2)180°      where n = # of edges

  2. The sum of all exterior angles = 360°

  3. Given a n-sided polygon with vertices located at (xi, yi), where i = 1, ..., n, and the vertices are arranged in a clockwise or anti-clockwise direction,

Area = n-1 (xiyi+1 - xi+1yi) + (xny1 - x1yn)
S
i=1

 

 

 

 

 

 

 

 

 

 

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