A polygon is a closed, two-dimensional shape formed by straight line segments. It must have three or more sides. The number of sides is the single most important factor used to classify and name every polygon.
The Core Definition: What is a Polygon?
A polygon is defined by a specific set of rules that govern its structure in a plane. It must be a closed figure, meaning the line segments connect end-to-end without any gaps. These straight line segments are known as the sides.
The points where two sides meet are called vertices, and these vertices define the shape’s interior angles. For a figure to qualify as a polygon, its sides cannot cross or intersect each other, and it must exist entirely within a two-dimensional plane.
The minimum requirement of three sides ensures that the figure can be closed and contain an area. The number of vertices and the number of interior angles will always be exactly equal to the number of sides.
The Naming Convention: From Sides to Names
The system for naming polygons uses Greek numerical prefixes to indicate the number of sides. The most familiar polygon is the triangle, which uses the prefix tri- to denote its three sides.
Moving up, a four-sided polygon is known as a quadrilateral, while the five-sided shape is a pentagon. The six-sided figure is a hexagon, and the seven-sided shape is called a heptagon. This systematic naming continues to define the shape based on its count of sides.
An eight-sided polygon is an octagon, a nine-sided shape is a nonagon, and a ten-sided shape is a decagon. For polygons with a large number of sides, these shapes are often referred to simply as an $n$-gon, where $n$ represents the specific number of sides, such as a 17-gon.
Key Distinctions: Regular vs. Irregular Polygons
Once a polygon is named based on its number of sides, it can be further classified by the relationship between its sides and angles. A regular polygon is defined by the condition that all its sides are equal in length and all its interior angles are equal in measure.
The square is a common example of a regular quadrilateral. In contrast, an irregular polygon is any polygon where the sides and/or the angles are not all equal.
A rectangle, for instance, is an irregular quadrilateral if its adjacent sides have different lengths. Similarly, a rhombus is irregular if its interior angles are not equal, even though all its sides are the same length.