Area Of Hexagon

A hexagon is a closed polygon made up of six line segments and six internal angles. For a hexagon, the sum of internal angle always adds up to \(720^{\circ}\).

 

Regular Hexagon

Regular Hexagon

 

According to the length of sides, the 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 of unequal length and angles are of unequal measures.

Area of Hexagon Formula

The area of the Hexagon has been derived as follows:

Area Of Hexagon

1) In the first step, we consider a regular Hexagon with the side length of ‘s’.

regular Hexagon with side length s

2) In the second step, we divide the regular hexagon into six equal parts by connecting the opposite vertices with the other vertices. When you observe it, you can see that the hexagon is divided into six different triangles.

3) We know that the 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 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, the formula for the area of the hexagon is obtained.

Similarly, for other polygons such as octagon, pentagon etc. we can also compute the area.

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

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