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What Are The Properties Of Polygons?

In geometry, polygons are defined as a flat shape or two-dimensional figure enclosed by three or more straight lines. A polygon consists of two words poly that means ‘many’ and gon that means ‘angle”. Here in this article, we will learn about the properties of polygons.

Different types of polygons and their properties:

1. Triangle: 

  •  It is formed by three line segments and has three vertices.
  • It has no diagonals.
  • The sum of all interior angles is 180

 2. Quadrilateral:

  • It is formed by four line segments and has four vertices.
  • It has two diagonals.
  • The sum of all interior angles is 360.

3. Pentagon:

  • It is formed by five line segments and has five vertices.
  • There are five diagonals in the pentagon.
  • The sum of all interior angles is 540

4. Hexagon:

  • It is formed by six line segments and has six vertices.
  • There are nine diagonals in a hexagon.
  • The sum of all interior angles is 720

5. Heptagon:

  • It is formed by seven line segments and has seven vertices.
  • There are fourteen diagonals.
  • The sum of all interior angles is 900

6. Octagon:

  • It is formed by eight line segments and has eight vertices.
  • There are twenty diagonals in this figure.
  • The sum of all interior angles is 1000

7. Nonagon:

  • It is formed by nine line segments and has nine vertices.
  • There are a total of twenty-seven diagonals. 
  • The sum of all interior angles is 1260

8. Decagon:

  • It is formed by ten line segments and has ten vertices.
  • There are a total of thirty-five diagonals.
  • The sum of all interior angles is 1440

Some other types of polygons:

  1. Regular Polygon: A polygon is said to be regular when all its sides and interior angles are equal.
  2. Irregular polygons: A polygon is said to be irregular when all its sides and interior angles are of different measures.
  3. Convex Polygon: A polygon is said to be convex when the sum of all interior angles is less than 180 and vertex points outward from the center of a figure.
  4. Concave Polygon: A polygon is said to be concave when one or more interior angles are more than 180 and vertex points inside of the figure.

Basic properties of polygons based on their sides and angles:

  1. The sum of all interior angles of a polygon having n-sides is (n-2)*180                    
  2. The number of diagonals in a polygon having n sides is n(n-3)/2
  3. The number of triangles that can be formed by joining diagonals from one corner of a polygon is n-2
  4. The Interior angle of a regular polygon having n-sides can be measured by [(n-2)*180 ]/n
  5. An exterior angle of a regular polygon having n-sides can be measured by 360 /n

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