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 Polygons
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 Polygons
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
Sides

Prefix 
20

Icosikai... 
30

Triacontakai... 
40

Tetracontakai... 
50

Pentacontakai... 
60

Hexacontakai... 
70

Heptacontakai... 
80

Octacontakai... 
90

Enneacontakai... 

+

Sides

Suffix 
+1

...henagon 
+2

...digon 
+3

...trigon 
+4

...tetragon 
+5

...pentagon 
+6

...hexagon 
+7

...heptagon 
+8

...octagon 
+9

...enneagon 

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.
