Hexagon Area Formula
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.
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.
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
Vedantu is a reliable platform for online learning resources and notes on a wide range of subjects and topics. At Vedantu 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 Vedantu 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
FAQs on Hexagon Formula
1. How to Calculate from an Irregular Hexagon?
One way to calculate the area of an Irregular Hexagon is with given vertices. That said, if you only know the vertices of the hexagon, you need to first create a chart with 2 columns and 7 rows. Next, label each row of the six points like (Point A, Point B, Point C, Point D, etc), and each column as the ‘x’ or ‘y’ coordinates of those points. Index the x and y coordinates of Point A to the right of Point A, Point B to the right of Point B, and so forth. Repeat the coordinates of the first point at the bottom of the index. Suppose, you’re working with the following points, in (x, y) pattern:-
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Multiply in x coordinates
A: (2, 6) [2 x 5] = 10
B: (1, 5) [1 x 8] = 8
C: (3, 8) [3 x 4] = 12
D: (7, 4) [7 x 6] = 42
E: (6, 6) [6 x 1] = 6
F: (10, 1) [10 x 6] = 60
A (again): (2, 6)
Summation is 138
Now, multiply in y coordinates
A: (2, 6) [6 x 1] = 6
B: (1, 5) [5 x 3] = 15
C: (3, 8) [8 x 7] = 56
D: (7, 4) [4 x 6] = 24
E: (6, 6) [6 x 10] = 60
F: (10, 1) [1 x 2] = 2
Summation is 163
Next, subtract the sum of the 2nd group from the sum of the 1st group of coordinates. Subtracting 163 from 138 = -25. Take the absolute value.
Now, dividing 25 by 2 will give you the Area of an irregular hexagon
25 / 2 = 12.5 square units ( area of an irregular hexagon is in square units)
2. Are Hexagon Tiles Used in Daily Life?
Hexagons are actually one of the most used polygons in the real world applications. These are used in tiles for flooring purposes. The hexagon is considered to be an excellent shape as it perfectly fits to cover any desired area.
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3. How to calculate the area of the Irregular Hexagon?
One of the ways of calculating the area of an Irregular Hexagon is by using the given vertices. However, if you only have data on vertices of the Hexagon then first you have to create a chart containing 2 columns and 7 rows. Then you must label each row of 6 points such as Point A, Point B, and so on. Each of the columns must be labeled on ‘x’ and ‘y’ coordinates of these points. Then index ‘x’ and ‘y’ coordinates of point A to the right side of Point A and so on. Repeat the coordinates of the first point at the index bottom.
4. Is there application of Hexagon tiles in daily life?
Yes, Hexagons are one of the widely used polygons in real-life situations and scenarios. The Hexagon tiles are extensively used for flooring. The Hexagon is fundamentally considered an excellent shape since it perfectly fits for covering the desired area in real-life applications. This is why you will find Hexagon tiles in numerous real-life applications including the tiles used for flooring in the buildings.
5. What is the difference between a Regular Hexagon and Irregular Hexagon?
The Regular Hexagon can be defined as the 6-sided polygon which is both equiangular and equilateral. This means that all the angles contained within the Hexagon have the same measurement and similarly the sides have the same length. The Irregular Hexagon, on the other hand, can be defined as the 6 sided polygon which is irregular, it implies that all sides and angles don’t have the same measure.
6. Are the Vedantu notes on “Hexagon Formula” reliable for exam studies?
Yes, the Vedantu notes on “Hexagon Formula” are extremely reliable as they are prepared by professional experts in the mathematics domain who have an excellent understanding of the subject. These notes provide a thorough explanation with solved examples, clear formatting, and lucid illustrations of the subject matter for helping the students understand the concept. Referring to these Vedantu notes can help the students in preparing efficiently for the exams.
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