# Regular Polygon Definition

In **Geometry**, almost all shapes are given specific names. In this category, a shape is termed a **Regular Polygon**. It is a specific type of Polygon that has **all sides of equal lengths** and **all angles of equal measure**.

Simply, we can say that a regular polygon is a **closed shape** with all sides and **angles** of **equal** measure. **For example**, a **square** is a regular polygon as it has **four equal sides** with all angles of **90 degrees**.

**Table of Contents**

**Note:**

Read about **Polygon** and Altitude in Geometry here.

## Requirements of a regular polygon

For calling a figure a regular polygon, it should fulfill the following requirements.

- It should be a closed shape.
- It should have all sides of equal lengths.
- All interior angles are of equal measure.

### What is the difference between a simple polygon and a regular polygon?

As mentioned above, a regular polygon is a specific type of polygon. So, what is the difference between a general polygon and a regular polygon? The only major difference between both figures is **the length and angle measures**.

All **closed shapes** are called **polygons** in Geometry. But a **regular polygon** has **sides** and **angles** with **equal** measures.

### Major parts of a regular polygon

It doesn’t matter whether we are talking about a general polygon or a regular one, it must have three major parts. Let us briefly explain them.

**Sides**: It includes those lines that are joining two vertices.**Vertex**: It is the point where two sides of a polygon meet.**Angles**: A polygon has both interior and exterior angles.

**Note:**

Read about **Sides**, Vertex, and **Angles** here.

**Examples of a Regular Polygon**

In geometry, all closed shapes are polygons but a few of those are termed regular polygons. Here is the list of the most popular regular polygons.

**Regular Pentagon:**: It is a shape that has**5 sides**with**5 angles**of equal measure.**Regular Hexagon**: It is a**6-sided**figure that makes a total interior angle of**720 degrees**.**Equilateral Triangle**: It is a particular type of triangle that has**three equal sides**with all angles of**60 degrees**.**Square**: It is a**quadrilateral**with**four**equal sides which make an angle of**90 degrees**with each other

**Note:**

Read about **Quadrilaterals** in detail.

### Operations on a Regular Polygon

Like all other shapes, a few operations are also implemented on a Regular Polygon. These are used to find the Area and **Perimeter** of the polygon. Here we are going to show you how to find Area and Perimeter.

**How to find the Area of a Regular Polygon?**

To find the area of a regular polygon, you can use the following formula.

A = (l^{2}n)/(4 tan〖π/n〗 )

Here:

**“l”**is the length of a side.**“n”**is the number of sides.

**How to find the Perimeter of a Regular Polygon?**

You can also find the Perimeter of a regular polygon that is also simple than the above formula. As a regular polygon has all sides of equal measures, you only have to add lengths of all sides to find Perimeter. Here is the general formula to find the Perimeter of a regular polygon.

P = nl

Here:

**“l”**is the length of a side.**“n”**is the number of sides.

### FAQ's

**Is a rectangle a regular polygon?**

No, a rectangle is not a regular polygon because it has only two sides with equal lengths.

**Is the circle a polygon?**

No, the circle is not a polygon even though it is a closed shape.

**How to check if a polygon is regular or not?**

To check this, you only have to measure the lengths of the sides and their concerning angles. If the lengths and angles measures are same, it means that a polygon is regular otherwise not.

**Why rhombus is not a regular polygon?**

A rhombus is not a regular polygon because all sides are of different measures.