# Regular polygon definition and properties

Learn the definition of a regular polygon. As we know the definition of the polygon, now we will learn what is a regular polygon and its properties. It is a very easy topic in geometry. Everybody can understand without any confusion. Now I will give the definition and also I will list some of the regular polygons with their internal angles.

## Definition of a regular polygon:

The given polygon in which if all the sides and also all the angles are equal then that polygon is called as a regular polygon.

Example: In the above diagram, we observe that all the three angles equal to ${ 60 }^{ 0 }$ and the three sides are equal to 5 cm. As all the angles and all the sides are equal so it is called as regular polygon.

### The important Properties of a regular polygon:

→For a regular polygon, each exterior angle is equal to $\frac { { 360 }^{ 0 } }{ n }$, where “n “is the number of sides of a polygon.

→The each interior angle of a regular polygon is equal to $\frac { \left( n-2 \right) \times { 180 }^{ 0 } }{ n }$.

→The sum of all the interior angles of a polygon is given by (n-2) × ${ 180 }^{ 0 }$.

→The sum of all the exterior angles of any given polygon is = ${ 360 }^{ 0 }$.

#### Some regular polygons diagrams: In the above diagram, all the angles of a quadrilateral and also all the sides are equal. So by this, we can say that this is a regular polygon. In quadrilateral, only square is a regular polygon.

As all the angles are equal to ${ 108 }^{ 0 }$ and all the sides are equal to 5 cm so this is a regular pentagon. Here all angles are equal to ${ 120 }^{ 0 }$ and all the sides are equal to 6 cm so this is called regular Hexagon. All the angles equal to ${ 128.6 }^{ 0 }$ and all sides are equal to 8cm so this is called regular Heptagon. Here all angles are equal to ${ 135 }^{ 0 }$ and all sides are equal to 6 cm so this is called regular Octagon. All the angles are equal to ${ 140 }^{ 0 }$ and all sides are equal to 3 cm so this is called regular Nonagon. Here all the angles are equal to ${ 144 }^{ 0 }$ and all the sides are equal to 3 cm so it is called regular Decagon.  