Properties of Hexagon

A polygon is a geometrical shape enclosed with straight lines. It is a two-dimensional shape and a common example of a polygon is a square or a rectangle. Moreover, polygons can be regular and irregular in shape. A regular polygon is a polygon that has equal sides as well as equal angles. While an irregular polygon is a polygon that does not have equal sides and therefore, the angles are also not equal. 

Geometry is one of the most interesting sections of geometry, the craze of getting your own geometry box to perform little experiments on the paper. We at Vedantu believe in keeping that excitement and curiosity intact within every child. In this article, we shall be discussing one such important topic of geometry that is the properties of Hexagon. 

Table of Content: 

• Properties of Hexagon - an introduction

• What are the Properties of Hexagon?

• Special Properties of Hexagon

• Frequently asked questions

Hexagon Properties Geometry

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 =√(332)

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

Special Properties of Hexagon

• 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 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 is 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 middle of the hexagon sides. Similar to circumradius, the radius of the incircle is called inradius that is formed by 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.