Regular Hexagon: Properties, Area & Perimeter Formulas

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Regular hexagon has six equal sides, six equal angles and has a closed shape. In a regular polygon, all the sides and angles of a polygon are equal. For example, a heptagon has 7 equal sides and a regular decagon has 10 equal sides. Any other closed figure or shape with curved lines are not considered as polygons; they are irregularly shaped figures. If we arrange six equilateral triangles, then a regular hexagon is formed and the area of the regular hexagon which is formed by the three equilateral triangles will be equal to six times the area of the same triangle.

Regular hexagon

Table of Content

Types Of Hexagon
Properties Of Regular Hexagon
Area Of Regular Hexagon
Perimeter Of Regular Hexagon
Angles Of Regular Hexagon
Things to Remember
Solved Questions

Keywords Takeaways: Polygon, Quadrilateral, Triangle, Area, Perimeter

Types Of Hexagon

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There are 4 types of Hexagon, which are explained below.

Regular Hexagon: They are those closed shaped hexagons whose all sides and angles are equal.

Irregular Hexagon: They are those closed shaped figures whose sides and angles are not equal or those hexagons that are not regular.

Concave Hexagon: They are those hexagons whose interior angles i:e one interior angle or more than one interior angle is greater than 180 degrees.

Convex Hexagons: They are those hexagons which have no interior angles greater than 180 degree.

Types Of Hexagon

Types of Hexagons

Read More:

Types of Polygons	Triangles	Area of Polygons

Properties Of Regular Hexagon

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Regular Hexagon has 6 equal sides.
Regular Hexagon has 6 equal angles.
A regular hexagon has 6 vertices.
Sum of interior angles of a hexagon is equal to 720 degrees.
A regular Hexagon is made of 6 equilateral triangles.
Interior Angle of a regular hexagon is equal to 120 degrees.
The External angle of a regular hexagon is equal to 60 degrees.
A regular hexagon has 9 diagonals.

Properties of Hexagon

Properties of Hexagon

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Isosceles Triangle Theorems	Difference between Sequence and Series
Differential Equation	Differentiation and Integration Formula

Area Of Regular Hexagon

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Area of a regular hexagon can be defined as the total amount of space covered inside a regular hexagon. Area of regular hexagon can be calculated by using the below given formula:

Area of Regular Hexagon = A = 3\(?3/2\) × a²

A = 2.59807 a²

Where ‘a’ is the length of the side of a regular hexagon.

Read More:

Surface Area of Rectangular Prism	Types of Triangles	Triangle Theorems

Perimeter Of Regular Hexagon

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Perimeter of a regular hexagon can be defined as the sum of all sides of a hexagon. Its Perimeter can be calculated by using the below given formula:

Perimeter P = 6a

Where ‘a’ is the length of a regular hexagon.

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Perimeter of Parallelogram	Laws of Vector Addition	Vector Formula

Angles Of Regular Hexagon

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Sum of all 6 interior angles of a regular hexagon is 720 degrees. So, to find the interior and the exterior angle of a regular hexagon can be calculated as follows:-

Interior Angle of a regular hexagon = 720°/ 6

Interior Angle of a regular hexagon = 120°

Exterior Angle of a regular hexagon = 180°- interior angle

Exterior Angle of a regular hexagon = 180°-120°

Exterior Angle of a regular hexagon = 60°

Read Also:

Parallelogram	Types of Polygon	Quadrilaterals

Things To Remember

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A regular hexagon has six equal sides and six equal angles and a regular hexagon has a closed shape.
Interior Angle of a regular hexagon = 120°
Exterior Angle of a regular hexagon = 60°
Area of Regular Hexagon = A = 3√3/2 × a²

A = 2.59807 a²

Perimeter of Regular Hexagon:- P = 6a
Regular hexagon has 9 diagonals.
Regular hexagons have 6 vertices.

Also Read:

Properties of Triangle	Isosceles triangle	Triangles Important Questions

Sample Questions

Ques: Find the Area and the Perimeter of a regular hexagon whose all sides are equal to 8cm. (2 marks)

Ans: Let ‘a’ be the length of the hexagon

Given that a = 8 cm

By applying the area and perimeter formula,

Area of a regular hexagon = 2.59807 a²

A = 2.59807 ( 8*8)

A = 166.27 Sq. cm

Perimeter = 6a

Perimeter = 6* 8

Perimeter = 48

Ques: Find the length of the side of a regular hexagon if its perimeter is given as 48cm. (3 marks)

Ans: It is given that the perimeter of a regular hexagon is 48 cm

Let the length of the side of a hexagon be ‘l’

Now we know that the formula for finding the perimeter is

Perimeter of a hexagon = 6 l

Therefore, substituting the values in the above formula we get,

Perimeter = 6*l

48 = 6 * l

L = 48 / 6

L = 8 cm

Hence the length of the regular hexagon is equal to 8 cm

Ques: Write down the five properties of a regular hexagon. (3 marks)

Ans: Five properties of a regular hexagon are as follows:-

Regular Hexagons have all 6 equal sides and 6 angles.
Sum of interior angles of a hexagon is equal to 720 degrees.
A regular Hexagon is made of 6 equilateral triangles.
Interior Angle of a regular hexagon is equal to 120 degrees.
The External angle of a regular hexagon is equal to 60 degrees.

Ques: The Area of a regular hexagon is 93.5 sq. cm, find the length of the regular hexagon. (3 marks)

Ans. It is given that the AREA of a regular hexagon is 93.5 sq cm

Let the length of the side of a hexagon be ‘ L’

Now we know that the formula for finding the AREA is

Area of a hexagon = 2.59807 a²

Therefore, substituting the values in the above formula we get,

93.5 = 2.59807 L2

L = √ 93.5 / 2.59807

L = 5.9

OR, L = 6 CM

Hence, the length of the regular hexagon is 6 cm

Ques: Find the number of sides of a regular polygon whose measure of each exterior angle is 60 degrees? (2 marks)

Ans: Total measure of exterior angles = 360 degrees

Measure of each exterior angle = 60 degrees

hence , the no of exterior angle = 360 / 60

the no of exterior angle = 6

Therefore, no of sides of a polygon = 6

Hence the required polygon is a Hexagon with 6 sides.

Ques: Find the Area and the Perimeter of a regular hexagon whose all sides are equal to 17 cm. (3 marks)

Ans: Let ‘a’ be the length of the hexagon

Given that a = 17 cm

By applying the area and perimeter formula,

Area of a regular hexagon = 2.59807 a²

A = 2.59807 ( 17*17 )

A = 750.84 Sq. cm

Perimeter = 6a

Perimeter = 6* 17

Perimeter = 102

Ques: Write down the different types of hexagon? (2 marks)

Ans: There are 4 types of Hexagon, let's have a look at them one by one

Regular Hexagon:- They are those closed shaped hexagons whose all sides and angles are equal are classified as Regular Hexagon.
Irregular Hexagon:- They are those closed shaped figures whose sides and angles are not equal or those hexagons which are not regular are known as Irregular hexagons.
Concave Hexagon:- They are those hexagons whose interior angles i:e one interior angle or more than one interior angle is greater than 180 degree are known as concave hexagons.
Convex Hexagons:- They are those hexagons which have no interior angles greater than 180 degree are classified as convex hexagons.

Ques: Find the number of sides of a regular polygon whose measure of each interior angle is 120 degrees? (2 marks)

Ans: Total measure of exterior angles = 720 degrees

Measure of each exterior angle = 120 degrees

hence , the no of exterior angle = 720 / 120

the no of exterior angle = 6

Therefore, no of sides of a polygon = 6

Hence the required polygon is a Hexagon with 6 sides.

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Tangents and Normals	Integral Calculus	Approximations
Types of Functions	Binary Operations	Coplanar Vector
Signum Function	Properties of Determinants	Maxima and Minima
Methods of Integration	Integration by Partial Fractions	Integration by Parts
Definite Integral	Fundamental Theorem of Calculus	Application of Integrals
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Probability	Conditional Probability	Multiplication Theorem of Probability
Pythagoras Theorem	Area of a Triangle	Area of Equilateral Triangle
Similarity of Triangles	Isosceles Triangle Theorem	Properties of Parallel Lines
Probability	Geometrical Shapes	Circles

Regular Hexagon: Properties, Area & Perimeter Formulas

Types Of Hexagon

Properties Of Regular Hexagon

Area Of Regular Hexagon

Perimeter Of Regular Hexagon

Angles Of Regular Hexagon

Things To Remember

Sample Questions

CBSE X Related Questions

1.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

3.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

6.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

Similar Mathematics Concepts

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Regular Hexagon: Properties, Area & Perimeter Formulas

Types Of Hexagon

Properties Of Regular Hexagon

Area Of Regular Hexagon

Perimeter Of Regular Hexagon

Angles Of Regular Hexagon

Things To Remember

Sample Questions

CBSE X Related Questions

1.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

3.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

6.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

3.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

6.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.