Nonagon

What is Nonagon?

In geometry, we may come across different types of polygons as shown in the figure given below. All of these polygons have different properties based on the number of sides and angles they have. A nonagon is a nine sided polygon and it is also called an Enneagon or 9-gon. In other words, a nonagon is a nine sided closed two dimensional figure.

Here, a 3-sided polygon is a triangle, 4 sided polygon is a quadrilateral, 5-sided polygon is a pentagon, 6-sided polygon is a hexagon, 7-sided polygon is heptagon, 8-sided polygon is octagon, 9-sided polygon is called a nonagon and a 10-sided polygon is the decagon.

Nonagon shape

A nonagon contains 9 straight sides and 9 vertices connecting these sides. The sum of all the interior angles of a nonagon is equal to 1260 degrees.

The above figure shows the shape of a nonagon that has 9 sides.

Nonagon shape images

Nonagons can be classified into regular and irregular nonagons.

Regular Nonagon

A nonagon with all sides congruent and equiangular is called a regular nonagon. The shape of a regular nonagon is given below.

Properties of Regular Nonagon

Some of the important properties of regular nonagon are listed below.

• The measure of each interior angle of a regular nonagon is equal to 140 degrees.

As mentioned above, the measure of each internal angle of a regular nonagon is 140° and the measure of the central angle is 40° when it is divided into triangles as shown in the above diagram. Also, the sum of all the exterior angles is 360 degrees.

• A regular nonagon can be divided into 9 isosceles triangles with equal area, that means 9 congruent isosceles triangles.
• The perimeter of a regular nonagon with side “a” is equal to 9a.
• The area of a regular nonagon of side length a is given by
  
  A = (9/4)a2 cot(π/9)
  
  Or
  
  A = (9/2)ar = 9r2 tan(π/9)
  
  Here, r is the radius of the inscribed circle of the regular nonagon and r = (a/2) cot(π/9).
  
  Or
  
  A = (9/2)R2 sin(2π/9)
  
  Here, R is the radius of the circumscribed circle of the regular nonagon.

Irregular Nonagon

A nonagon in which all sides are not equal and all angles are not equal. However, the sum of all its interior angles is always 1260° even if it has irregular sides and unequal angles. Some of the irregular nonagon shapes are given below.

How many sides are in a nonagon

As the name denotes, a nonagon has 9 sides, since nona means nine and gon means sides.

Here, AB, BC, CD, DE, EF, FG, GH, HI and AI are the 9 sides of the above nonagon.

Diagonals of Nonagon

The number of diagonals of a nonagon is equal to 27. These diagonals can be observed from the below diagram.

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