**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 “.

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