 # Area Of Hexagon Formula ### Definition :

A polygon with six sides and six angles is termed as a Hexagon. Similarly, we have Pentagon where the polygon has 5 sides; Octagon has 8 sides.Each internal angle of the hexagon has been calculated to be 102o .

In general, the sum of interior angles of a Polygon is given by-

$\mathbf{ (n-2) \times 180}$

A Hexagon can be of two types, Namely

• Regular Hexagon
• Irregular Hexagon

In case of former one, all the sides are of equal length and the internal angles are of the same value. The regular hexagon consists of six symmetrical lines and rotational symmetry of order of 6.

Whereas in the case of the latter one, neither the sides are equal, nor the angles are same. Regular Hexagon Irregular Hexagon

Area of the hexagon is the space confined within the sides of the polygon.

### Area of Hexagon:

The area of Hexagon is given by

Area of Hexagon = $\large \frac{3 \sqrt{3}}{2}x^{2}$

where “x” denotes the sides of the hexagon.

There is one more formula that could be used to calculate the area of regular Hexagon:

Area= $\large \frac{3}{2} .d.t$

Where “t” is the length of each side of the hexagon and “d” is the height of the hexagon when it is made to lie on one of the bases of it.

Similarly, if we are to find the area of the polygons- like area of a regular pentagon, area of octagon-

Area of Pentagon:

Area of Regular Pentagon= $\large \frac{1}{4}\sqrt{5 + 2 \sqrt{5}} a^{2}$

Where ‘a’ denotes the length of the each side of the pentagon.

Area of Octagon:

Area of Regular Octagon = $\large 2(1+ \sqrt{2})a^{2}$

Where ‘a’ denotes the length of the each side of the octagon.

### Solved Example

Question 1: Find the area of a hexagon whose side is 4 cm and radius is 6 cm?
Solution:
Given,
s = 4 cm
r = 6 cm
Area of a hexagon
= 3 × s × r
= 3 × 4 × 6 cm2
= 72 cm2

This is all about 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 our site or download BYJU’S-The Learning App.