Double Math

# 9 Sided Polygon (Nonagon) – Nine Sided Shape

## What is a Nine 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  “nine-sided shape “.

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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: In gardening, a nonagon shape might be considered for a better view.

## 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)</p> <p>[katex] Area=\frac94\;\left(64\;\right)\left(3.0777\right)

Area= 554.784 square units