Area of Hexagon Formula

A polygon having six sides and six angles is called a Hexagon. Regular hexagons have six equal sides and six angles and are composed of six equilateral triangles. There are a variety of ways to calculate the area of a hexagon, whether you're working with an irregular hexagon or a regular hexagon.There are various ways to determine the area of hexagon formula . The various methods are mainly based on how you spit the hexagon. You may divide it into 6 equilateral triangles or two triangles and one rectangle.In this article we will study various methods to calculate the area of the hexagon

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Where s is the sides of the hexagon

Types of Hexagon

Types of hexagona can be classified as follows:

• Regular Hexagon

• Irregular Hexagon

In the case of a regular hexagon, all the sides are of equal length and the internal angles are of the same value.Whereas in the case of irregular hexagons, neither the sides are equal, nor the angles are the same.

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Regular Hexagon Irregular Hexagon

How to Find the Area of a Hexagon?

There are several ways to find the area of a hexagon.

1. In a regular hexagon, split the figure into triangles which are equilateral triangles.

2. Find the area of one triangle.

3. Multiply this value by six.

Alternatively, the area can be found by calculating one-half of the side length times the apothem.

Formula for the Area of a Hexagon

The area of Hexagon formula is given by

Area of Hexagon = 3√3/2 x s2

where “s” denotes the sides of the hexagon.

Second area of regular hexagon formula is given by:

Area of Hexagon = 3/2 x s x h

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

Method 1

One of the easiest methods that can be used to find the area of a polygon is to split the figure into triangles. Let's start by splitting the hexagon into six triangles. 

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In this figure, the center point,x, is equidistant from all of the vertices. As a result, the six dotted lines you can say diagonals within the hexagon are of the same length. Likewise, all of the triangles within the hexagon are congruent by the side-side-side rule: each of the triangle's share two sides inside the hexagon as well as a base side that makes up the perimeter of the hexagon. In a similar fashion, each of the triangles have the same angles. There are 

3600 in a circle and the hexagon in our image has separated it into six equal parts; therefore, we can write the following:

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θ=3600/6

θ=600

We also know the following:

∠AXB=∠BXC=∠CXD=∠DXE=∠EXF=∠FXA=600

Now, let's look at each of the triangles in the hexagon. We know that each triangle has two two sides that are equal; therefore, each of the base angles of each triangle must be the same. We know that a triangle has 180 and we can solve for the two base angles of each triangle using this information.

2x + 600 = 1800

2x = 1200

x = 600

Each angle in the triangle equals 600

We now know that all the triangles are congruent and equilateral: each triangle has three equal side lengths and three equal angles. Now, we can use this vital information to solve for the hexagon's area. If we find the area of one of the triangles, then we can multiply it by six in order to calculate the area of the entire figure. 

We have, Area of equilateral triangle = (√3/4) x s x s

So, Area of hexagon = 6 x (√3/4) x s  x s 

+= 3 x (√3/2) x s x s

Area of Hexagon = 3 √3/2 x s2

Method 2

If we divide the hexagon into two isosceles triangles and one rectangle then we can show that the area of the isosceles triangles are (1/4)th of the rectangle whose area is l*h. 

So, area of regular Hexagon formula is given by:

Area= (3/2) x h x s

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

Solved Examples

Example 1: Find the area of a regular hexagon whose side is 7 cm.

Solution:   

Formula of regular hexagon is = 3√3/ 2 x s2

where, s = side =  7 cm

Substitute the value of side in area formula,

Area = (3 x 1.7320) / 2 x 7 x 7

= 127. 31 cm2.

Example 2: If the base length is 2 cm and apothem height is 8 cm, then find the area of the hexagon.

Solution: Formula of regular hexagon = (3/2) × s × h

Here apothem height is given so we need to multiply it by 2 and substituting the value in the above formula, we get

= (3/2) × 2 × (8*2)

=  48cm2.