A hexagon is a six-sided polygon with the sum of internal angles as 720o. If you look at a hexagon, you can see that it consists of triangles. Some day to day objects that are hexagonal in shape are a honeycomb, floor tiles, bolt head, etc. A regular hexagon has equal angles and equal sides. Moreover, there are two types of the hexagon- convex hexagon and concave hexagon.

A convex hexagon is similar to a regular hexagon as it has interior angles lesser than 180o.

While a concave hexagon is opposite to convex as it has one or more than one angle greater than 180o.

The area of a regular hexagon can be calculated using a formula developed by theorists. The formula is given below:

A = \[(\frac{3\sqrt{3}}{2})\]s2 ; where

A - is the area of the hexagon

s - is the length of each side

Moreover, the perimeter for a regular hexagon can also be calculated by a formula that is mentioned below:

Perimeter = 6s; where

s - is the length of each side

Moving forward there are some special properties of the hexagon that are unique to this polygon and they shall be discussed further in this article

The first and most important property of a regular hexagon is that it has six sides. Hexa means six and therefore a hexagon is supposed to have six side.

The next property is in continuation of the first property. As there are six sides, there are also six angles in a hexagon.

The lengths of each side of a regular hexagon are equal.

The angles of each side of a regular hexagon are equal.

A regular hexagon has nine diagonals.

Since all angles are equal in a regular hexagon, each angle is 120o and the summation of all the interior angles is 720o.

In terms of exterior angles, all the angles are again equal in a regular hexagon. The summation of all exterior angles is 360o with each angle equal to 60o.

A regular hexagon also has six axes of symmetry. Three of these axes pass through diagonals opposite to the vertices and the remaining three pass through the middles of opposite edges.

When a straight line is drawn from the center of a regular hexagon that joins one of its vertices, it can lead to the formation of six identical triangles.

The central angle of each of these triangles is 60o. Also, the remaining two angles are also 60o. Therefore, it can be concluded that these are equilateral triangles. A regular hexagon is formed of 6 equilateral triangles that are identical in terms of lengths and angles of each side.

Another important property of a hexagon is circumcircle. A regular polygon has six vertices which can form a circle connecting these vertices. This is a circle is called a circumscribed circle or circumcircle of the polygon. The center of this circle is the same as the center of the polygon. Similarly, the radius of the circumcircle if the distance from the center to the vertex of the polygon. This radius is referred to as circumradius. Likewise, the diameters of the circumcircle are the same as the diameter of the hexagon.

Apart from the circumcircle, there is another circle that can be formed in a hexagon. This circle is called an incircle. As the name suggests, this circle is inscribed in the hexagon and is formed through the middles of the hexagon sides. Similar to circumradius, the radius of the incircle is called inradius that is formed lines connecting the center of the hexagon with the sides or vertex. The center for the circle is the same as the center of the hexagon. Moreover, the incircle is tangent to all six sides of the hexagon.

There are various properties of a hexagon. Some of the major properties of a regular hexagon are its equal sides, equal angles, nine diagonals, circumcircle, and incircle. Moreover, it is necessary to know about the angles, interior, and exterior, of a regular hexagon. Further applications of these properties have been observed in trigonometry, coordinate geometry, and also when calculating the area of a hexagon or parts of a hexagon.

FAQ (Frequently Asked Questions)

1. What are the Real-Life Examples of a Hexagon and what is the Difference Between a Regular and Irregular Hexagon?

A hexagon is a two-dimensional geometrical shape. It has six sides with a unique geometrical shape on its own. Some common real-life examples of the hexagon are a honeycomb, shape of floor tiles, and bolt head. A regular hexagon has an equal length of each side as well as angles. While an irregular hexagon is the opposite of that. It has sides that differ in length from each other and so do the angles.

2. Give the formula for the area and perimeter of a hexagon. Are equilateral triangles present in the structure of the hexagon? If yes, then how many.

The formula of the area of the hexagon is

A = (3√3 / 2)s^{2} ; where

A - is the area of the hexagon

s - is the length of each side

The formula for the perimeter of a hexagon is

P= 6s; where

s - is the length of each side.

Yes, we can find equilateral triangles of 60^{o} in the geometric structure of a hexagon. A total of 6 equilateral triangles can be found in a hexagonal structure.