Subject: Geometry

Polygon Basics

What is a polygon?

Wikipedia defines polygon as a flat shape consisting of straight lines that are joined to form a circuit. It is basically a plane figure that is bounded by a closed path. This path is composed of line segments. These line segments are what is called the edge or sides of the polygon. The points where these line segments that forms the path meet, is called the vertex of the polygon.


A triangle is an example of a polygon because it is a closed figure whose sides are made up of line segments.

The word "polygon" comes from two Greek word polus and gonia. Polus means many or much while gonia means corner or angle. Thus, a polygon means many angles or many corners.

Identifying polygons.

To give you a visual look at what are polygons, look at the figure below. Only two figures are polygons while others are not.

In the figure above, the first shape from the left is not a polygon. Even though its sides are made up of line segments, it is not closed, so it can't be a polygon. Also not polygons are the second and fifth shape if the figure above. Though they are closed, some sides are not made up of line segments. In fact, some sides or edges are made up of curves. Thus, they are not polygons too. Only the third and fourth figures are polygons.

Naming polygons

Basic classifications of polygons are made by referring to the number of sides or edges or line segments a certain kind of polygon has. For example, a triangle is a polygon with three sides so it can be named tri-gon or triangle. Tri means three sides and trigon means a polygon with three sides. So for polygons with five sides, it is classified as heptagon. Hexagon for six sides and so on. So generally, n-gon are polygons with n sides. Refer to the list below for a list of the first few classifications of polygons.

Classification of Polygons*

Shape

Nomenclature

Number of Edges or Sides

triangle or tri-gon

3

tetragon or square

4

pentagon

5

hexagon

6

heptagon

7

octagon

8

nonagon

9

decagon

10

hendecagon

11

dodecagon

12

n

n-gon

n

*This classifications of polygons only applies to regular types of polygons. Types and kinds of polygons will be discussed below.

Types and kinds of polygons

Different types of polygons are classified into three categories.

1. Regular and Irregular Polygons

If all of the polygon's sides or edges or angles are the same, then they are called regular polygons. Otherwise, its irregular polygons.

2. Simple and Complex Polygons

When the polygon's sides or edges does not cross over or overlap each other, it is called simple. When edges do intersect, then it is called a complex polygon.

3. Convex and Concave Polygons

Convex polygons happen if there are any angle inside the polygon which measures more than 180 degrees. Convcave polygons on the other hand is when all angles inside are less than 180 degrees.