 # Polygon Definition

In Geometry, a polygon is a closed two-dimensional figure, which is made up of straight lines. Generally, from the name of the polygon, we can easily identify the number of sides of the shape. For example, a triangle is a polygon which has three sides. Here, let us discuss the polygon definition, types of a polygon, its formula, properties with an example.

## Polygon Definition in Maths

In Mathematics, a polygon is a closed two-dimensional shape having straight line segments. It is not a three-dimensional shape. A polygon does not have any curved surface. A polygon should have at least three sides. Each side of the line segment must intersect with another line segment only at its endpoint. Based on the number of sides of a polygon, we can easily identify the polygon shape. The list of polygon shapes with the number of sides is given below.

 No. of Sides Polygon Shape 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon

## Types of Polygon

Based on the angle measure and the sides of a polygon, the polygon is classified into:

• Regular Polygon – All the interior angles and the sides are equal
• Irregular Polygon – All the interior angles and the sides are of different measure
• Convex polygon – All the interior angles of a polygon are strictly less than 180 degrees
• Concave Polygon – One or more interior angles of a polygon are more than 180 degrees

## Polygon Formula

The important polygon formulas are:

1. The sum of interior angles of a polygon with “n” sides =180°(n-2)
2. Number of diagonals of a “n-sided” polygon = [n(n-3)]/2
3. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n
4. The measure of exterior angles of a regular n-sided polygon = 360°/n

### Polygon Properties

The important properties of the polygon are

• The sum of interior angles of all the quadrangles is equal to 360 degrees.
• If at least one of the interior angles is greater than 180 degrees, then it is called concave
• If a polygon does not cross over itself, and has only one boundary, it is called a simple polygon. Otherwise, it is a complex polygon

### Polygon Example

Question:

Find the sum of the interior angle of a pentagon

Solution:

We know that a pentagon has five sides.

The formula to find the sum of interior angles is given by:

Interior angle sum = 180°(n-2)

= 180°(5-2)

= 180° (3)

= 540°

Hence, the sum of the interior angles of a pentagon is 540°