A hexagon is defined as a closed 2D shape that is made up of six straight lines. It is a two-dimensional shape with six sides, six vertices, and six interior angles. The name is divided into 'hex', which means six, and 'gonia', which means corners. Let us learn about hexagon shape in detail in this article.
|1.||What is Hexagon?|
|3.||Sides of a Hexagon|
|4.||Angles of Hexagon|
|5.||Diagonals of a Hexagon|
|6.||Types of Hexagon|
|7.||Properties of Hexagon|
|8.||FAQs on Hexagon Shape|
What is Hexagon?
Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon shape are a hexagonal floor tile, pencil cross-section, clock, a honeycomb, etc. It can be either regular (with 6 equal side lengths and equal angles) or irregular (with 6 unequal side lengths and angles).
A regular hexagon is defined as a closed 2D shape made up of six equal sides and six equal angles. Each angle of the regular hexagon measures 120 degrees. And the sum of all the interior angles is 120 × 6 = 720 degrees. When it comes to the exterior angles, we know that the sum of exterior angles of any polygon is always 360°. There are 6 exterior angles in a hexagon. So, each of the exterior angles in a regular hexagon measures 360 ÷ 6 = 60 degrees.
A regular hexagon is different from an irregular hexagon as in an irregular hexagon, there is no definite measurement of angles, and the lengths of sides are different. Some of the properties that are common to both irregular and regular hexagons are given below:
- There are 6 sides, 6 interior angles, and 6 vertices in both.
- The sum of all 6 interior angles is always 720 degrees.
- The sum of all 6 exterior angles is always 360 degrees.
Sides of a Hexagon
There are six sides of a hexagon, as shown in the above figure. All are straight edges and form a closed shape. In a regular hexagon, we have six equal sides, while in an irregular hexagon, at least two of the sides of a hexagon are different in measure. If we take the sum of all six sides, we will get the perimeter of the hexagon.
In a regular hexagon, if we know the value of perimeter, then the length of each side can be calculated as "Perimeter ÷ 6". For example, if the perimeter of a regular hexagon is 72 units, then the length of each of the hexagon sides is 72 ÷ 6 = 12 units.
Angles of Hexagon
There are six interior angles and six exterior angles in a hexagon. The sum of all six angles of hexagon is 720 degrees, while the sum of its exterior angles is 360 degrees. Look at some properties related to hexagon angles listed below:
- The measurement of each interior angle in a regular hexagon is 720° ÷ 6 = 120°.
- The measurement of each exterior angle of a regular hexagon is 360° ÷ 6 = 60°.
- At least two of the angles are of different measurements in an irregular hexagon.
Diagonals of a Hexagon
A diagonal is a segment of a line, that connects any two non-adjacent vertices of a polygon. The number of diagonals of a polygon is given by n(n-3)/2, where 'n' is the number of sides of a polygon. The number of diagonals in a hexagon is given by, 6 (6 - 3) / 2 = 6(3)/2, which is 9. Out of the 9 diagonals, 3 of them pass through the center of the hexagon.
There are basically two types of diagonals in a hexagon which are: Long diagonals (3 diagonals that pass through the center), and short diagonals. The length of each long diagonal in a regular hexagon can be measured using the formula '2s'. And the length of each short diagonal can be measured using the formula '√3s', where s is the length of each side of the hexagon.
Types of Hexagon
Hexagons can be classified based on their side lengths and internal angles. Considering the sides and angles of a hexagon, the types of the hexagon are:
- Regular Hexagon: It is one that has equal sides and angles. All the internal angles of a regular hexagon are 120° each. The exterior angles measure 60° each. The sum of the interior angles of a regular hexagon is 6 times 120°, which is equal to 720°. The sum of the exterior angles is equal to 6 times 60°, which is equal to 360°.
- Irregular Hexagon: It has sides and angles of different measurements. All the internal angles are not equal to 120°. But, the sum of all interior angles is the same, i.e 720 degrees.
- Convex Hexagon: It is one in which all the interior angles measure less than 180°. Convex hexagons can be regular or irregular, which means they can have equal or unequal side lengths and angles. All the vertices of the convex hexagon are pointed outwards.
- Concave Hexagon: It is one in which at least one of the interior angles is greater than 180°. There is at least one vertex that points inwards.
Properties of Hexagon
A hexagon is a flat two-dimensional shape with six sides. It may or may not have equal sides and angles. Based on these facts, the important properties of a hexagon are as follows:
- It has six sides, six edges, and six vertices.
- All the side lengths are equal or unequal in measurement.
- All the internal angles are equal to 120° each in a regular hexagon.
- The sum of the internal angles is always equal to 720°.
- All the external angles are equal to 60° each in a regular hexagon.
- The sum of the exterior angles is equal to 360°.
- The number of diagonals (a line segment joining two non-adjacent vertices of a polygon) that can be drawn is 9.
- A regular hexagon is also a convex hexagon since all its internal angles are less than 180°.
- It can be split into six equilateral triangles.
- It is symmetrical as each of its side lengths is equal.
- The opposite sides of a regular hexagon are always parallel to each other.
- The area of a regular hexagon is 3√3a2/2 square units, where a is the side length.
- The hexagon's perimeter can be found by adding the lengths of all six sides.
☛ Related Topics
Check out some interesting articles related to hexagon shape in math.
Example 1: What is the area of a regular hexagon of side 3 units?
Area of a regular hexagon = 3√3a2/2 square units.
Given, side 'a' = 3 units.
Therefore, area = 3(√3)32/2
= (3 × √3 × 9) /2
= (27× √3) / 2
= 23.38 square units
Therefore, the required area is 23.38 square units.
Example 2: Find the length of each side of a regular hexagon, if its area is 150√3 square units.
Applying the formula of area of a regular hexagon,
Area = 3√3a2/2 square units
Therefore, 150√3 = 3√3a2/2
300√3 = 3√3a2
Canceling √3 on both sides,
300/3 = a2
100 = a2
a = √100
Therefore, the length of each side is 10 units.
Example 3: What is the length of each side of a regular hexagon, if its perimeter is equal to 108 units?
Given, the perimeter = 108 units.
Since it is a regular hexagon, all its sides are of equal length. To find the length of each side, we just need to divide the perimeter by 6.
⇒ Perimeter ÷ 6
⇒ 108 ÷ 6
= 18 units
Therefore, the length of each of the hexagon sides is 18 units.
FAQs on Hexagon
What is a Hexagon Shape?
A hexagon is a two-dimensional flat shape that has six angles, six edges, and six vertices. It can have equal or unequal sides and interior angles. It is a 6-sided polygon classified into two main types - regular and irregular hexagon.
What are the Angles of a Hexagon?
A hexagon has six angles and the sum of all six interior angles is 720 degrees. In a regular hexagon, each interior angle measures 120 degrees.
What is a Regular Hexagon?
A regular hexagon is defined as a special type of hexagon that has all sides equal. All six angles in a regular hexagon are also equal.
How many Sides does a Hexagon have?
A hexagon has six sides. All six sides joined together and form a closed shape known as a hexagon. In a regular hexagon, all six sides are of equal lengths, while in an irregular hexagon, there is no definite relationship between the sides as they are different in measure.
What is the Perimeter of a Hexagon?
The perimeter of a hexagon is the sum of its boundary. It is the sum of all six sides. In the case of a regular hexagon, the formula to calculate its perimeter is 6 × side length.
What is an Irregular Hexagon?
An irregular hexagon has at least one unequal side and angle when compared to the other sides and angles. There is no definite measurement of each of the angles, but the sum of all 6 interior angles is always 720 degrees, and the sum of all 6 exterior angles is 360 degrees.
What are the Three Attributes of a Hexagon?
The three attributes of a hexagon are:
- It has 6 sides
- It has 6 angles
- It has 6 vertices
Does a Hexagon Always Have Equal Sides?
Hexagon may not necessarily have all sides equal. It can have sides of variable lengths too. The hexagon having equal sides is called a regular hexagon and the one with different sides is called an irregular hexagon.
How are Hexagons Classified?
A hexagon is classified based on the side lengths and angles. Based on this, hexagons are classified into regular (equal side-lengths and angles) and irregular (unequal side-lengths and angles) hexagons. It can also be classified as convex and concave hexagons. Convex hexagons are the ones in which all the interior angles are less than 180° and concave hexagons are the ones in which at least one of the interior angles is greater than 180°.
What is the Sum of Interior Angles of a Hexagon?
In a hexagon, the sum of all 6 interior angles is always 720º. The sum of interior angles of a polygon is calculated using the formula, (n-2) × 180°, where 'n' is the number of sides of the polygon. Since a hexagon has 6 sides, taking 'n' as 6 we get. (6-2) × 180°, which gives 720°.
How many Diagonals can be Drawn in a Regular Hexagon?
The formula to calculate the number of diagonals of a polygon is n(n-3)/2, where 'n' is the number of sides of the polygon. A hexagon has 6 sides. therefore, the number of diagonals is 6(6-3)/2, which is equal to 9.
How many Lines of Symmetry are there in a Regular Hexagon?
For all regular polygons, the number of lines of symmetry is equal to the number of sides. Thus, for a regular hexagon, there are six lines of symmetry.
How to Find the Area of a Hexagon?
We can determine the area of a hexagon by identifying the length of the side of the hexagon. To find the area of a regular hexagon we use the formula, A = (3√3 S2)/2 square units, where S is the length of one side.
What is the Formula to Calculate the Perimeter of a Hexagon?
The formula to calculate the regular hexagon perimeter is 6a units, where 'a' is the side length of the hexagon. In the case of an irregular hexagon, we add the side lengths. Mathematically, it can be expressed as,
Perimeter of hexagon = (a + b+ c+ d + e + f) units.