The Perimeter of Hexagon Formula

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The Formula of Perimeter of Hexagon

Hexagon is a two-dimensional closed figure made up of six line segments. It is a polygon with six sides and the measurement of six sides is equal. As all the sides of a hexagon are equal, its perimeter will be calculated by multiplying the length of each side by 6. Each internal angle of the hexagon is measured as 120 degrees. For example, if the length of each side of the hexagon is given as ‘a’, then the perimeter of the hexagon formula will be given as 6 × a. Hence, the formula of the perimeter of the hexagon is given as:


The perimeter of Hexagon Formula = 6 × Side


The area of a hexagon is the space of a region occupied by a hexagon. Read the article below to know the methods and formula to find the area of the hexagon.


What is Hexagon?

In Geometry, the hexagon is a two-dimensional polygon with six sides and six angles. The word hexagon is derived from the Greek word ‘Hex’ meaning ‘ six’, and gonia meaning ‘ corner angles’.


Let's discuss some real-life examples of hexagon:

Cells in beehives and snowflakes given below have a hexagonal shape as both have six straight sides.


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Area of Hexagon

The area of the hexagon is the space occupied within its perimeter. The grey coloured area in the figure below represents the area of the hexagon.


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Area of Hexagon Formula

Given all the sides of the hexagon equal, the formula to find the area of the hexagon is:


\[A = \frac{3\sqrt{3}}{2} \times s^{2}\]


Area of Hexagon Formula Example

1. Find the area of a hexagonal board whose perimeter is 24 cm

Solution:

Given: Perimeter of the board = 24 cm

The perimeter of hexagon = 6 × side

Substituting the values,

24 = 6 × a

a = 4

Hence, the hexagonal side length = 4 cm

Let's calculate the area of the hexagon. As we know,

Area of Hexagon = \[\frac{3\sqrt{3}}{2} \times S^{2}\]

Substituting the values,

Area of hexagon = \[\frac{3\sqrt{3}}{2} \times 4^{2}\]

A = 41.47 cm²

Therefore, the area of the hexagonal board is 41.47 cm².


Types of Hexagon

The two types of hexagon are:

  1. Regular Hexagon

  2. Irregular Hexagon

Regular Hexagon: A regular polygon is a two - dimensional closed figure with six equal sides and angles. The measurement of each interior angle of the hexagon is 120°.

Irregular Hexagon: An irregular polygon is a two - dimensional closed figure with six unequal sides and angles. In other words, a hexagon that is not a regular polygon is considered an irregular hexagon.

Let us now learn how to find the perimeter and area of a regular hexagon with examples.


The Perimeter of Regular Hexagon Formula

The perimeter of a regular hexagon is the sum of the length of all its sides. To find the premiere of a regular hexagon, we must be aware of the number of sides of a hexagon which is 6.


As the number of sides of a regular hexagon is 6, therefore, we can calculate the perimeter of a regular hexagon by multiplying the number of sides by 6. Accordingly, the perimeter of the regular hexagon formula is given as:


Hexagonal Formula  Perimeter =  6 × Side


Let’s understand with an example below:

Find the perimeter of a regular hexagon with side length 6 cm.

Solution:

Using the perimeter of regular hexagon formula given the side length with n = 6 cm, we have:

Perimeter (P) = 6 × side length

Substituting the value we get,

6 × 6 = 36 cm


The perimeter of Regular Hexagon = 36 cm


Area of Regular Hexagon

Let say, each side of a regular hexagon is s cm. To find the area of a regular hexagon, whose side length is s cm, we use the following area of a regular hexagon formula:


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Area of regular Hexagon = \[\frac{3\sqrt{3}}{2} \times S^{2}\]


Let's understand with an example:

Example:

1. Find the area of a regular hexagon whose side length is 12 cm.

Solutions:

Using the area of regular hexagon formula given the side length with n = 12 cm, we have:

Area of regular hexagon = \[\frac{3\sqrt{3}}{2} \times Side^{2}\]

Substituting the value we get,

\[\frac{3\sqrt{3}}{2} \times 12^{2}\]

\[\frac{3\sqrt{3}}{2} \times 144\] 

\[= 3\sqrt{3} \times 72\]

\[= 216\sqrt{3}\]

A = 374.1 cm²

Area of Regular Hexagon = 374.1 cm²


Conclusion

Now recall the information which you have learned in this article and answer the following questions:

  • How to define the area and perimeter of a hexagon?

  • How to calculate the area and perimeter of a regular hexagon?

The formulas to find the area and perimeter of a hexagon given on this page will not only help you to solve geometry problems but also you can easily determine the area and perimeter of hexagonal shapes that exist in real life.

FAQ (Frequently Asked Questions)

Q1. What are the Properties of the Hexagon?

Ans: Some of the properties of the hexagon are:

  1. All the six sides of the hexagon are equal in length.

  2. The measurement of the interior angles of the hexagon is equal to 120 degrees.

  3. The sum of all interior angles of the hexagon is equal to 720 degrees.

  4. The measurement of all the six angles of a hexagon is equal.

Q2. What are Real-Life Examples of the Hexagon?

Ans: Some of the real-life examples of the hexagon are:

  • The cells of the beehive are hexagonal.

  • The collection of tiny lenses that are present in dragonfly eyes are hexagon in shape.

  • Humble snowflakes found in nature are hexagon in shape.

  • Nuts and bolts are the most common examples of hexagonal shape.

  • The shape of pencils is a hexagon.

Q3. What are the Four Different Types of Hexagon?

Ans: The four different types of hexagon are:

  1. Regular hexagon

  2. Irregular hexagon

  3. Convex hexagon

  4. Concave hexagon