What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (2024)

Home » Math Vocabulary » Hexagon – Definition, Types, Properties, Examples, FAQs

  • What is a Hexagon?
  • Types of Hexagons
  • Classification of hexagons based on their angles
  • Solved Examples on Hexagon
  • Practice Problems On Hexagon
  • Frequently Asked Questions On Hexagon

What is a Hexagon?

In geometry, a hexagon can be defined as a closed two-dimensional polygon with six sides.

Hexagon has 6verticesand 6angles also.

Hexa means six and gonia means angles.

Examples

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (1)
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (2)

Non – Examples

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (3)
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (4)

Hexagon in Real Life

We can find the shape of a hexagon in a honeycomb, a football, face of pencil, and floor tiles.

Hexagon around us

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (5)

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (6)Begin here

2d Shapes

Identify Trapezoid, Hexagon, and Pentagon Game

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Types of Hexagons

Hexagonal shape is classified into several types based on the measure of sides and angles.

Classification of hexagons based on their sides

1. Regular Hexagon

When the length of all the sides and measure of all the angles are equal, it is aregular hexagon. All interior angles of a regular hexagon are 120 degrees each.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (8)

Properties of a Regular Hexagon

  • All the sides are equal in length.
  • All the interior angles measure 120°.
  • All the exterior angles measure 60°.
  • Since all angles are equal in a regular hexagon, each angle is 120o and the sum of all the interior angles is 720o.
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (9)
  • A regular hexagon can be divided into six equilateral triangles.
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (10)
  • The opposite sides of a regular hexagon are parallel to each other.
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (11)
  • A regular hexagon is also a convex hexagon.

Symmetry in regular hexagon:

A regular hexagon has 6 lines of symmetry and a rotational symmetry of order 6

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (12)
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (13)
6 lines of symmetrySix 60° angles of rotation

2. Irregular Hexagon

In an irregular hexagon, the length of sides and measure of angles do not have the same measure.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (14)

Related Worksheets

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Classification of hexagons based on their angles

1. Convex Hexagon

For convex hexagons, all of its interior angles must be less than 180 degrees, and all the vertices are pointed outwards. Convex hexagons can be regular or irregular.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (17)
What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (18)

2. Concave Hexagon

For concave hexagons, at least one of its interior angles must be greater than 180° and at least one of its vertex points inwards.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (19)

Properties of Hexagon

  • It is two-dimensional.
  • It has six sides, six edges and six vertices.
  • The sum of the interior angles is 720 degrees.
  • It has nine diagonals.

Perimeter of a Hexagon

The perimeter of a hexagon is the sum of the length of all 6 sides.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (20)

Perimeter = AB + BC + CD + DE + EF + FA

In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (21)

Perimeter = a + a + a + a + a + a = 6a

Solved Examples on Hexagon

Example 1: Find the perimeter of a regular hexagon having each side measure 20 cm.

Solution:

Perimeter of regular hexagon = 6 × length of side

= 6 × 20 cm

= 120 cm

So, the perimeter of the hexagon is 120 cm.

Example 2: The perimeter of a regular hexagon is 36 cm. What is the length of its sides?

Solution:

Perimeter of regular hexagon = 6 × length of side

36 = 6 × length of side

Length of side = 366 cm = 6 cm

So, the length of its sides is 6 cm.

Example 3: Five angles of a hexagon measure 110° each. What is the measure of the sixth angle?

Solution:

Sum of the interior angles in hexagon = 720°

Sum of five angles = 5 × 110° = 550°

Sixth angle = 720° – 550° = 170°

So, the measure of the sixth angle is 170°.

Practice Problems On Hexagon

1

What is the measure of each interior angle of a regular hexagon?

60°

100°

120°

720°

CorrectIncorrect

Correct answer is: 120°
The sum of the interior angles of a hexagon is 720° For a regular hexagon all the sides are of the same length and all interior angles are equal. So, each interior angle= 720/6 = 120° So, the measure of the interior angle of a regular hexagon is 120°.

2

A plane with six sides is classified as

pentagon

hexagon

heptagon

octagon

CorrectIncorrect

Correct answer is: hexagon
Hexagon is a two dimensional polygon with six sides.

3

The hexagon is said to be convex hexagon if none of its interior angles is

90°

less than 90°

more than 90° and less than 180°

more than 180°

CorrectIncorrect

Correct answer is: more than 180°
more than 180° For convex hexagons, all of its interior angles must be less than 180 degrees. For concave hexagons, at least one of its interior angles must be greater than 180°.

4

A regular hexagon has how many lines of symmetry

4

6

8

9

CorrectIncorrect

Correct answer is: 6
A regular hexagon has 6 lines of symmetry. In a regular polygon the lines of symmetry are equal to the number of sides. So there will be 6 lines of symmetry for a regular hexagon.

Frequently Asked Questions On Hexagon

There are four types of hexagons. These are regular hexagons, irregular hexagons, concave hexagons, and concave hexagons.

Hexagon has 6 sides, 6 angles and 6 vertices.

The sum of all interior angles of a hexagon is 720°.

A hexagon has 9 diagonals.

No, hexagons can have sides with different lengths. Regular hexagon has all sides are equal in length.

Yes, all six sided shapes are called hexagons.

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts (2024)

FAQs

What is a Hexagon? Definition, Properties, Area, Perimeter, Facts? ›

A hexagon is a two-dimensional shape with six sides and six points, or vertices. In a regular hexagon, the sides are all equal in length and the sum of all of the internal angles is equal to 720°, or 120° each. The center point of a hexagon is equidistant from the outside points of the hexagon.

What are the properties and definition of hexagon? ›

It has six sides and six angles. Lengths of all the sides and the measurement of all the angles are equal. The total number of diagonals in a regular hexagon is 9. The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees.

What is the perimeter and area of a hexagon? ›

The formula that is used to calculate the area of a regular hexagon is (3√3 s2)/2; where 's' is the side length. The perimeter of a hexagon can be calculated by adding all six side lengths. In the case of a regular hexagon, we use the formula, Perimeter = 6 × s; where 's' is the length of one side.

What is the definition of a regular hexagon? ›

A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal. For instance, a regular pentagon has 5 equal sides and a regular octagon has 8 equal sides.

How do you fully define a hexagon? ›

In geometry, a hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles also. Hexa means six and gonia means angles. We can find the shape of a hexagon in a honeycomb, a football, face of pencil, and floor tiles.

What is the short answer of hexagon? ›

In geometry, a hexagon is a closed two-dimensional six-sided polygon. It is made up of six line segments and six vertices that form six internal angles. The sum of all the internal angles of a hexagon is 720°.

Are hexagons the strongest shape? ›

The list of structures from strongest to weakest are: (1) cylinder (averaging 164.8 kg of load at crushing weight), (2) hexagon (averaging 136.8 kg of load at crushing weight), (3) square (averaging 127 kg of load at crushing weight), (4) triangle (averaging 89.2 kg of load at crushing weight).

Do all hexagons have 6 equal sides? ›

No, not all hexagons have equal sides. A hexagon is a polygon with six sides, but its sides can have different lengths. A hexagon with equal sides is called a regular hexagon. In a regular hexagon, all six sides are the same length, and all six angles are equal.

What is the perimeter area of a hexagon? ›

Perimeter is the distance around the outside of a shape. For example, if you walk around the edge of a playground, you're measuring its perimeter. Area is the amount of space inside a shape.

What is the formula for a hexagon? ›

FAQs on Hexagon Formula

The hexagon formula calculates the perimeter, area, and diagonals of the hexagon. The hexagon formulas apply directly to regular hexagons. The hexagon formulas are given as, Area of hexagon = (3√3s2)2 ( 3 3 s 2 ) 2 and Perimeter of hexagon = 6s, where s = side length.

What are the properties of a hexagon? ›

Properties of Regular Hexagon

The properties of a regular hexagon include: Six sides: A regular hexagon has six equal-length sides. Six angles: Each angle of a regular hexagon measures 120 degrees. All angles in a regular hexagon are congruent.

What are the 4 types of hexagon? ›

All hexagons have six sides, regardless of the type of hexagon it is. This means that regular hexagons, irregular hexagons, concave hexagons and convex hexagons all have six sides each.

Which shape has 8 sides? ›

In geometry, Octagon is a polygon that has 8 sides and 8 angles. That means the number of vertices and edges of an octagon is 8, respectively. In simple words, the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane.

What is the definition and properties of an octagon? ›

In geometry, Octagon is a polygon that has 8 sides and 8 angles. That means the number of vertices and edges of an octagon is 8, respectively. In simple words, the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length.

What is a defining attribute of a hexagon? ›

The three attributes of a hexagon are: It has 6 sides. It has 6 angles. It has 6 vertices.

What is the scientific definition of a hexagon? ›

hexagon, in geometry, a six-sided polygon. In a regular hexagon, all sides are the same length, and each internal angle is 120 degrees.

What is a hexagon elementary definition? ›

A hexagon is a two-dimensional shape with six sides and six angles. That also means that hexagons are polygons. Polygons are flat two-dimensional shapes with straight sides. Polygons enclose a space, and they do not have any curved sides.

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