What is a Polygon?.

The word polygon is a combination of two Greek words: "poly" means many and "gon" means angle. Along with its angles, a polygon also has sides and vertices. "Tri" means "three," so the simplest polygon is called the triangle, because it has three angles. It also has three sides and three vertices. A triangle is always coplanar, which is not true of many of the other polygons.

Basically, polygons are many-sided figures, with sides that are line segments. They are named according to the number of sides and angles they have. The most common polygons are the triangle, rectangle and the square.

A regular polygon is one that has equal sides, like a square, equilateral triangle etc.
Polygons also have diagonals, which are segments that join two vertices and are not sides

The table lists all the polygons having up to 10 sides. (it is extracted from www.math.com)

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 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.

Formulas relating to polygons
(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)