Polygon and its Types

Introduction

Polygon term originates from the two Greek words “Poly” and “Gon”, where “Poly” stands for “many” and “Gon” stands for angle. So the complete word “Polygon” deals with shapes having many angles.

Interestingly, number of angles in a shape is always equal to the number of edges or sides it may have. In short, we can say a polygon is a shape with many sides or angles.

So, what are the various types of polygons in geometry and how they are made?

Not to go so far, we use curves to make various shapes in geometry. So, to draw all polygons we use curves. Polygon has its angels, edges, vertices and diagonals. We can visualise them and see how many are they in any polygon.

What is a Curve?

Curve is a plain figure which is made by joining a number of points without lifting a pencil from paper and without retracing any portion of drawing.

Moreover, a curve which do not intersect itself is called open curve and on the other hand, a curve which intersect itself is called closed curve.

Different types of curves
Different types of curves

What is a Polygon in Geometry?

Polygon is a closed curve which is made up of only finite number of line segments and any two line segments do not intersect each other except at their end points. It is a two dimensional figure in geometry.

The line segments of a polygon are called sides or edges and end points of the line segments are called its vertices or corners.

Different types of polygon
Different types of polygon

What are Adjacent Sides?

Any two sides of a polygon with a common end point are called adjacent sides of the polygon.

What are Adjacent Vertices?

The end points of a side of a polygon are called adjacent vertices.

What is a Diagonal of polygon?

A diagonal is a line segment which is formed by joining two vertices which are not adjacent.

Example

AC is a diagonal. BD is a diagonal.

Diagonals
Diagonals

Types of polygon

Convex polygon

A polygon is said to be a convex polygon, if its diagonals completely lie inside of it. Its all interior angles are less than 180 degree.

Concave polygon

A polygon is said to be a concave polygon, if its diagonals completely lie outside of it. Its one or more than one interior angle is more than 180 degree.

Regular polygon

A regular polygon is a polygon whose all sides and all angles are equal. In other words we can say, it is both equilateral and equiangluar.

Example

Square is a regular polygon as its sides are equal and all angles are equal.

Formula

Interior angle of regular polygon

\(= (n-2)*180^o\)

or

\(= (n-2)*\pi radian\)

Irregular polygon

Polygon which is not a regular polygon, i.e. if it is not equiangular and not equilateral is called irregular polygon.

Example

Rectangle is a irregular polygon.

Simple polygon

It is a flat shape consisting of straight and non intersecting line segments that are joined to form a single close path. A Simple Polygon does not cross over itself. It is also called Jordan Polygon.

Classification of polygon based on number of sides

Number of sides of polygon Name of polygon Number of angles of polygon
3 Triangle 3
4 Quadilateral 4
5 Pentagon 5
6 Hexagon 6
7 Heptagon 7
8 Octagon 8
9 Nonagon 9
10 Decagon 10