What is a Polygon?
A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.
Types  Formulas  Parts  Special Polygons  Names
Types of Polygon
Regular – all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular – all angles are equal.
Equilateral – all sides are the same length.
Convex – a straight line drawn through a convex polygon crosses at most two sides. Every interior angle is less than 180°.  
Concave – you can draw at least one straight line through a concave polygon that crosses more than two sides. At least one interior angle is more than 180°. 
Polygon Formulas
(N = # of sides and S = length from center to a corner)
Area of a regular polygon = (1/2) N sin(360°/N) S^{2}
Sum of the interior angles of a polygon = (N – 2) x 180°
The number of diagonals in a polygon = 1/2 N(N3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N – 2)
Polygon Parts
Side – one of the line segments that make up the polygon.
Vertex – point where two sides meet. Two or more of these points are called vertices. Diagonal – a line connecting two vertices that isn’t a side. Interior Angle – Angle formed by two adjacent sides inside the polygon. Exterior Angle – Angle formed by two adjacent sides outside the polygon. 
Special polugons
Special Quadrilaterals – square, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles – right, equilateral, isosceles, scalene, acute, obtuse.
Polygon Names
Generally accepted names
Sides

Name 
n

Ngon 
3

Triangle 
4

Quadrilateral 
5

Pentagon 
6

Hexagon 
7

Heptagon 
8

Octagon 
10

Decagon 
12

Dodecagon 
Names for other polygons have been proposed.
Sides

Name 
9

Nonagon, Enneagon 
11

Undecagon, Hendecagon 
13

Tridecagon, Triskaidecagon 
14

Tetradecagon, Tetrakaidecagon 
15

Pentadecagon, Pentakaidecagon 
16

Hexadecagon, Hexakaidecagon 
17

Heptadecagon, Heptakaidecagon 
18

Octadecagon, Octakaidecagon 
19

Enneadecagon, Enneakaidecagon 
20

Icosagon 
30

Triacontagon 
40

Tetracontagon 
50

Pentacontagon 
60

Hexacontagon 
70

Heptacontagon 
80

Octacontagon 
90

Enneacontagon 
100

Hectogon, Hecatontagon 
1,000

Chiliagon 
10,000

Myriagon 
To construct a name, combine the prefix+suffix

+


Examples:
46 sided polygon – Tetracontakaihexagon
28 sided polygon – Icosikaioctagon
However, many people use the form ngon, as in 46gon, or 28gon instead of these names.
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