[Maths Class Notes] on Hexagon Formula Pdf for Exam

In Euclidean geometry, the polygon is a 2D – two-dimensional closed shape that has many sides. Each side has a straight segment. The Hexagon is the type of polygon that consists of 6 sides and angles. The Regular Hexagon consists of six sides and angles which are congruent and are made up using six equilateral triangles. The formula for finding the area of a Regular Hexagon is as follows: Area = (3√3 s²)/ 2 and here S is used for representing the length of the side of the Regular Hexagon. 

In Euclidean geometry, a polygon is a two-dimensional closed shape having many sides. Each side is a straight segment. A hexagon is a kind of polygon which has six sides and angles. A Regular hexagon has six sides and angles that are congruent and is made up of six equilateral triangles. The formula to find out the area of a regular hexagon is as given;  Area = (3√3 s²)/ 2 where, ‘s’ represent the length of a side of the regular hexagon.

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Methods of Calculating the Area of the Hexagon

There are different ways and methods of calculating the area of the Hexagon, regardless of if you are working with the, or Regular Hexagon. Here we will have a brief look at one of the methods in which you can find the area of the Hexagon.

Method 1: Calculating using the given side length

In this method, first, you need to note the formula for the area of a Regular Hexagon and then input the length of the side that we already know. If you do not know the length of the side then you can find it by following this stepwise approach.

1. Calculate the length of the side.

If you only have the perimeter, then you must divide it by 6 to obtain the length of one of the sides. If you only know apothem, you can still find out the length of sides by using apothem in the formula a = x √3 and then you must multiply the result with 2. This is because the apothem shows x√3 sides of the 30-60-90 triangle which it forms. 

2. Put the value of side length in the formula.

From the mentioned length of one side of the triangle is 8, and then you can just put 8 in the original formula, such as: Area = (3√3 x 8²)/2. Here we get the 3√3 x 64/2. 

Now, 192√3/2 = 166.27. Here it is worth noting that the value of √3 is about 1.732.

In method 2 you can calculate with the given apothem. In the 1st step of this method, the formula is used for finding the area of the Hexagon with the given apothem. In the next step, the apothem is used for finding the perimeter. And finally, in the last step, all the known values are plugged into the formula.

Solved Examples of the Hexagon Formula

is a reliable platform for online learning resources and notes on a wide range of subjects and topics. At you can find accurate and reliable solved examples of the Hexagon that can help you understand the concept even better and give you the required practice needed for the preparation of the exams. For solved examples on Hexagon Formula, you can refer to the note here. 

How to Calculate Area of Regular Hexagon Formula?

There are different ways to calculate the area of a hexagon, whether you’re working with a regular hexagon or an irregular hexagon. Check below to find the number of ways with which you can easily find the area of the hexagon.

Method 1: Calculate with a Given Side Length

Firstly, write down the area of the regular hexagon formula and insert the length of a side you already know. However, if you are not aware of the length of a side but are given the length of the perimeter or apothem (the height of one of the equilateral triangles created by the hexagon, Which is perpendicular to the side), you can still calculate the length of the side of the hexagon. Here’s how to do it step-by-step:

1. Calculate the Length of a Side:

If you are only given the perimeter, just divide it by 6 to obtain the length of one side. As an example, if the length of the perimeter is 48 cm, then divide it by 6, you get 8cm, the length of the side.

If you only know the apothem, you can still find the length of a side by plugging the apothem into the formula a = x√3 and then multiplying the outcome by 2. It is because the apothem depicts the x√3 sides of the 30-60-90 triangle that it forms. If the apothem is 15√3, for example, then x is 15 and the length of a side is 15 × 2, or 30.

2. Plug the Value of the Side Length into the Formula:

From the aforementioned length of one side of the triangle are 8, just plug 8 into the original formula, like this: Area = (3√3 x 8²)/2. We get 3√3 x 64/2

Then, 192√3/2 = 166.27

Note that the value of √3 is approximately 1.732

Method 2: Calculate with a Given Apothem

1. Use the Formula to Find the Area of a Hexagon with a Given Apothem:

The perimeter of the hexagon formula is simply: Area = 1/2 x perimeter x apothem. Let’s say the apothem is 7√3 cm.

2. Use the Apothem to Find the Perimeter

You already know that the apothem is perpendicular to the side of the hexagon; it forms one side of a 30-60-90 triangle. The sides of a 30-60-90 triangle are in the proportion of x-x√3-2x, where:-

• ‘X’ represents the length of the short leg of the triangle, which is through the 30° angle,

• x√3 represents the length of the long leg of the triangle, which is through the 60° angle, and

• 2x represents the hypotenuse of the triangle 2x

The apothem is the side denoted by x√3. Thus, we need to plug the length of the apothem into the formula a = x√3 and solve. As an example, if the apothem’s length is 7√3, plug it into the formula and obtain 7√3 cm = x√3, or x = 7 cm.

By simplifying for x, you have found the length of the short leg, 7. Since it depicts half the length of one side of the hexagon, multiply it by 2 to get the full length of the side i.e. 7 x 2 = 14 cm.

Since you know that the length of one side is 14cm, multiply it by 6 to find the perimeter of the hexagon: 14 cm x 6 = 84 cm

3. Plug All of the Known Values into the Formula

Now, all you need to do is plug the perimeter and apothem into the formula and solve:

Area = 1/2 x perimeter x apothem

Area = 1/2 x (84) x (7√3) cm

= 509.20 cm²

 

Solved Examples of Hexagon Formula

Example 1:

Find the area of the hexagon with given variables s = 7

Solution 1:

We know that the side length of a regular hexagon i.e. s = 7.

Now, we can find the area of the hexagon using the following formula:

(3√3 s²)/ 2

Let’s substitute the given value into the area formula for a regular hexagon and solve.

A = 3√3 7² / 2

Simplify.

= 3√3 49 / 2

= 147 √3 / 2

= 127.30

Round off the outcome to the nearest whole number.

A =127 cm²