polygon and its properties

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) S²

Sum of the interior angles of a polygon = (N - 2) x 180°

The number of diagonals in a polygon = 1/2 N(N-3)
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	N-gon
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 n-gon, as in 46-gon, or 28-gon instead of these names.