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.

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:

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 =  (l2 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.