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Hexagon is a polygon with six sides and six angles in geometry. It is a two-dimensional closed figure made up of six line segments. The name of Hexagon is derived from the Greek word ‘hex’ meaning six and ‘gonia’ meaning angles. If all the six sides and angles of a hexagon are equal, then the hexagon is called a regular hexagon. Each internal angle of a hexagon is 120 degrees and the external angle of a hexagon is 60 degrees. The perimeter of hexagon is calculated by multiplying one side of the hexagon by 6. Thus, the Perimeter of Hexagon Formula is 6 x a, where a refers to the length of the side of the hexagon.
Read More: NCERT Solutions for Class 6 Maths Mensuration
| Table of Content |
Key Terms: Hexagon, Perimeter of Hexagon, Regular Hexagon, Irregular Hexagon, Perimeter of Hexagon Formula, Angles, Sides
What is Hexagon?
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Hexagon is a two-dimensional polygon with six sides and six angles.
- There are various types of hexagon namely regular hexagon, irregular hexagon, convex hexagon, and concave hexagon.
- A regular hexagon is a hexagon whose all sides and angles are equal.
- There are a total of 9 diagonals in a hexagon.
- Each interior angle of a hexagon is 120 degrees.
- The sum of all the interior angles of a hexagon is 720 degrees.
- Each exterior angle of a hexagon is 60 degrees.
- The sum of all exterior angles of a hexagon is 360 degrees.
Hexagon
Read More:
| Relevant Concepts | ||
|---|---|---|
| Properties of Hexagon | Difference Between Area and Perimeter | Difference between Area and Volume |
| Area Perimeter Formula | Formula Of Perimeter Shapes | Area of Polygons |
Types of Hexagon
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Hexagons are generally of the following types:
- Regular Hexagon: In a regular hexagon all of its sides are equal in length.
- Irregular Hexagon: Hexagon in which all of its sides are not equal in length is considered to be an irregular hexagon.
- Concave Hexagon: A hexagon that has at least one angle of more than 180 degrees is called a concave hexagon.
- Convex Hexagon: A hexagon in which each angle is less than 180 degrees is called a convex hexagon.
Types of Hexagon
What is Hexagon Formula?
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Hexagon formula is defined as a set of formulas used to calculate the perimeter, and area of a hexagon.
- The sum of all the sides of a hexagon is defined as the perimeter of hexagon.
- The space occupied within the perimeter of a hexagon is defined as the area of a hexagon.
Read More: Mensuration MCQs
Perimeter of Hexagon Formula
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Perimeter of hexagon is the sum of the length of all its sides. The number of sides of a regular hexagon is 6, therefore, we can calculate the perimeter of regular hexagon by multiplying the number of sides by 6.
The perimeter of hexagon formula is given as
| Perimeter of Hexagon = 6 x a |
Here, a refers to the length of the side of the given hexagon.
In the case of an irregular hexagon, the perimeter would be the sum of all six sides.
How to Calculate Perimeter of Hexagon?
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We can calculate the perimeter of hexagon by following the given steps:
Perimeter of Regular Hexagon
- Find the length of one of the sides of the hexagon.
- Multiply the length of one side of the hexagon by 6. The value received will be the perimeter of regular hexagon.
Perimeter of Irregular Hexagon
- Find the length of each of the sides of the hexagon.
- Add up all the lengths of the sides and you’ll get the perimeter of an irregular hexagon.
Read More: Mensuration Formula
Solved ExamplesExample 1: What will be the perimeter of the regular hexagon with one side 12 cm. Solution: Given that, a = 12 cm Using the perimeter of hexagon formula, P = 6× a = 6 × 12 P = 72 cm Thus, the perimeter of a hexagon with each side 12 cm is 72 cm. Example 2: Calculate the perimeter of a hexagon with sides as 2 cm, 5 cm, 6 cm, 4 cm, 3 cm and 7 cm. Solution: The given hexagon is an irregular hexagon as all its sides are different. To find the perimeter of hexagon, we will add up all the sides. Perimeter of Hexagon = 2 cm + 5 cm + 6 cm + 4 cm + 3 cm + 7 cm = 27 cm Thus, the perimeter of hexagon is 27 cm. |
Area of Hexagon
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The area of hexagon refers to the total space occupied by a hexagon enclosed within its boundaries. The area of hexagon formula is
| \(\frac{3 \sqrt{3}}{2}\) x side2 |
Solved ExampleExample: Calculate the area of regular hexagon whose side length is 12 cm. Solution: It is given that the side of the hexagon is 12 cm. So, s = 12 cm. Using the area of hexagon formula, we get Area of Hexagon = (3√3)/2 x 122 = (3√3)/2 x 144 = 3√3 x 72 = 216√3 = 374.1 Thus, the area of hexagon is 374.1 cm2. |
Read More:
| Related Topics | ||
|---|---|---|
| Heptagon | Perimeter of a Square | Perimeter of a Kite |
| Perimeter of a Parallelogram | Perimeter of Rectangle | Perimeter of a Triangle |
Things to Remember
- Hexagon is defined as a polygon with six sides and six angles.
- Hexagons are generally of two types namely regular hexagon and irregular hexagon.
- A regular hexagon has six equal sides and six equal angles.
- The perimeter of hexagon is the sum of the lengths of the six sides of the hexagon.
- The perimeter of regular hexagon is 6 x a, where a is the side of the hexagon.
- The perimeter of an irregular hexagon is the total sum of all six sides of the hexagon.
Sample Questions
Ques. Calculate the perimeter of a regular hexagon whose each side is 6 cm. (3 Marks)
Ans. Given that.
Length of Side of Hexagon (a) = 6 cm
Using the perimeter of hexagon formula,
P = 6 x a
P = 6 x 6
P = 36 cm
Thus, the perimeter of the a regular hexagon with side 6 cm is 36 cm.
Ques. The perimeter of a regular hexagon is 27 inches. What is the length of each side? (3 Marks)
Ans. Let ‘a’ be the length of each side of a regular hexagon. As we know that the perimeter of a regular hexagon is the sum of all the sides = 27
Therefore,
6 x a = 27
a = 27/6
a = 9/2
a = 4.5
Hence each side of the given regular hexagon is 4.5 inches.
Ques. Find the perimeter of a hexagon with side lengths 9 cm, 10 cm, 14 cm, 13 cm, 12 cm, and 8 cm. (3 Marks)
Ans. As we know that,
The perimeter of an irregular hexagon is the sum of all its sides.
Therefore,
Perimeter of Hexagon = 9 + 10 + 14 + 13 + 12 + 8
Perimeter of Hexagon = 66 cm
Hence the perimeter of the irregular hexagon is 66 cm.
Ques. Differentiate between regular and irregular hexagons. (3 Marks)
Ans. Following are the major differences between a regular and an irregular hexagon-
- In a regular hexagon, all of its sides and angles are equal whereas in an irregular hexagon its sides and angles are unequal.
- To calculate the perimeter of a regular hexagon its side is multiplied by 6 and to calculate the perimeter of an irregular hexagon, first, we need to find the lengths of each of the sides and add up all the lengths of the sides.
Ques. Write down any five properties of a hexagon. (4 Marks)
Ans. The properties of a hexagon are as follows:
- In a regular hexagon the sum of all interior angles is 720 degrees and the sum of exterior angles is 360 degrees.
- Each interior angle of a regular hexagon is 120 degrees and each exterior angle of a hexagon is 60 degrees.
- The diagonals in a hexagon are 9.
- A regular hexagon can be divided into six equilateral triangles very easily.
- The opposite sides of a regular hexagon are always parallel.
Ques. Find out the perimeter of a hexagon whose side is given as 8 cm. (3 Marks)
Ans. It is given that the side of the hexagon is 8 cm.
Using the perimeter of hexagon formula,
P = 6 x a
P = 6 x 8
P = 48 cm
Thus, the perimeter of the given hexagon is 48 cm.
Ques. Write down any three properties of a regular hexagon. (3 Marks)
Ans. The properties of a regular hexagon are:
- A regular hexagon has six equal sides as well as six equal angles.
- It has 6 vertices and 9 diagonals.
- The perimeter of a regular hexagon is calculated by multiplying the length of the side of a hexagon by 6.
Ques. Calculate the side length of the regular hexagon whose perimeter is 24 units. (3 Marks)
Ans. Given that,
- Perimeter of Hexagon = 24 units
- Length of Side (a) =?
Using perimeter of hexagon formula,
Perimeter of Hexagon = 6 x s
24 = 6 × a
a = 24/6
a = 4 units
Thus, the length of the side of the hexagon is 4 units.
Ques. Explain the perimeter of hexagon formula. (2 Marks)
Ans. The perimeter is the measurement of the sum of the sides of a shape. The perimeter of a regular hexagon can be calculated by multiplying the side of a hexagon by 6.
Perimeter = 6 x Side
Ques. How to find the perimeter of a hexagon? (2 Marks)
Ans. Finding the perimeter of a hexagon will depend on whether the hexagon is regular or irregular. If the hexagon is regular, the length of one side will be multiplied by 6. If the given hexagon is irregular, then, each side must be added together to get the perimeter.
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