9 Sided Shape (Nonagon) 9 sided Polygon

What is a 9 Sided Shape?

With nine straight sides that meet at nine corners make a polygon that is called a Nonagon. Nonagon is a 2D nine-sided shape that belongs to the family. The word “nonagon ” comes from the Latin word “nona “, meaning nine, and “gon “, meaning sides. So it literally means “9 sided shape “.

There are 9 straight sides and 9 vertices connecting these straight sides in a nonagon. The Sum of all the interior angles of a nine-sided polygon is equal to 1260 degrees.

In Greek, a nonagon is called an enneagon, which means “nine corners”.

Types of (Nonagon) 9 Sided Shape

There are two types of nonagon.

Regular Nonagon
Irregular Nonagon

Regular Nonagon

It is a two-dimensional shape.
It has nine vertices.
Each interior angle is at $140^\circ$ and the sum of these interior angles is $1260^\circ$ .
It’s all straight lines that have equal lengths.
It has an exterior angle equal to 360 degrees.
The regular nonagon has a symmetrical appearance and is considered a highly geometrically structured shape. It’s often used to demonstrate principles of symmetry and equality in geometry.

Irregular Nonagon

The sum of all of its interior angles is $1260^\circ$ degrees.
Angles at varying degrees.
It is a nine-sided, two-dimensional shape
Additionally, it has straight lines
The sides are not equal in length.
Irregular nonagon does not have the symmetrical properties of a regular nonagon and can take on various shapes, making it more versatile in appearance.

9 sided Shapes in daily life and their role.

Nine sided Shape or nonagon used in various fields for example Stop sign is used to control traffic

Football: Some footballs are in nonagon shape that players use for better playing.

Garden: A nonagon shape might be considered for a better view in gardening.

Area of Nine-sided Shape (Nonagon) Examples

Question #1: Find the area of a regular nonagon with a side length of $8$ units.

The formula for the area of regular Nonagon is

$Area=\frac94\;l^2\;cot\left(\frac{\mathrm\pi}9\right)$

here $l$ is the length of each side of nonagon(regular)

so,

$Area=\frac94\;8^2\;cot\left(\frac{\mathrm\pi}9\right)   [latex] Area=\frac94\;\left(64\;\right)\left(3.0777\right)$

$Area= 554.784$ square units