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.

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°

Learn more Maths definitions and formulas by downloading BYJU’S – The Learning App