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