 # Area Of Hexagon

## Definition : Regular Hexagon

A Hexagon is a closed polygon made of six line segments  having six internal angles. For a Hexagon, the sum of internal angle always add up to $720^{\circ}$.

According to the Length of sides, Hexagon can be of two types,

(i) Regular Hexagon: A regular hexagon is the one whose all the 6 sides are equal in length. Also the internal angle is equal to $120^{\circ}$.

The regular hexagon consists of six symmetrical lines and rotational symmetry of order of 6.

(ii) Irregular Hexagon: An irregular hexagon is the one whose all the sides are not of equal length. Also the

## Area of Hexagon- Formula:

The area of the Hexagon has been derived as follows: 1) In the first step, we consider a regular Hexagon with the side length of ‘s’. 2) In the second step we divide the regular Hexagon into six equal parts by connecting the opposite vertices with one another. On closely observing we see that the Hexagon is divided into six different triangles by doing so.

3) We know that area of a right angled triangle is:

Area = $\frac{1}{2}.s.h$

Where s and h stand for the base and the height of the triangle respectively.

4) The Area of the each of the triangle has been computed in the step (3). As there are six similar triangles, therefore the total area of the desired Hexagon has been computed as:

Area of Hexagon = $6. \frac{1}{2}.s.h$ = $3.s.h$

Where $h^{2} = s^{2} – \left ( \frac{s}{2} \right )^{2}$

$h = \frac{\sqrt{3}}{2}s$

Therefore, Area of Hexagon = $h = \frac{3\sqrt{3}}{2}s^{2}$

Thus by the above formula area of the Hexagon is obtained.

Similarly for  other polygons such as octagon, etc. we can also compute the area in a similar fashion:

This is all about the formula to compute the area of Hexagon. To know more about the other characteristics and attributes of polygons such as Hexagon, pentagon, octagon so on and so forth and other geometrical figures, please do visit www.byjus.com or download BYJU’S-The Learning App.