How to find perimeter of hexagon

Polygon is nothing but a closed figure(end to end connected) made up of more than 2 line segments on a 2-dimensional plane. A polygon is created by using straight-line segments that are end to end connected with each other, and these line segments are known as sides of the polygon and the point is known as the vertex of the polygon.

Hexagon in a two-dimensional plane is an object that has six angles and six sides. In a hexagon all the sides and angles are equal. The total of the internal angles of any hexagon is 720°. A regular hexagon has 6 rotational symmetries and 6 reflection symmetries. All internal angles are 120°.  

We can define perimeter as the sum of the length of all six sides.

Perimeter = 6*s

where, s is the side of the hexagon.

Derivation:

We know that there are six sides and all those are equal. 

Consider the side as ‘s’. Then sum of six sides is s + s + s + s + s + s

So perimeter is 6s

Sample Problems

Question 1: Find the perimeter of the regular hexagon with one side 2 cm.

Solution:

Given that, length of one side = 2cm

so perimeter = 6*s

substitute s = 2

=> 6*2 = 12 cm

Therefore the perimeter of the regular hexagon with one side 2 cm is 12 cm.

Question 2: Find the perimeter of the regular hexagon with one side 10 cm.

Solution:

Given that, length of one side = 10cm

so perimeter = 6*s

substitute s = 10

=> 6*10 = 60 cm

Therefore the perimeter of the regular hexagon with one side 10 cm is 60 cm.

Question 3: One side of the pencil which is in hexagonal shape is 4 cm. what is the perimeter of the pencil?

Solution:

Given that, length of one side  of pencil = 4 cm

so perimeter = 6*s

substitute s = 4

=> 6*4 = 24 cm

Therefore the perimeter of the pencil with one side 4 cm is 24 cm.

Question 4: There are 4 nuts with each side as 2 cm and 8 bolts with 3 cm as each side. Find the perimeters of all nuts and bolts.

Solution:

We know that nuts and bolts are hexagonal shape. so

There are 4 nuts with each side as 2 cm

each nut perimeter is 6*s => 6 * 2 = 12 cm

So , Perimeter of all nuts  is 4 * 12 = 48 cm

There are 8 bolts with each side as 3 cm

each bolt perimeter is 6*s => 6 * 3 = 18 cm

So, Perimeter  of  all bolts  is 8 * 18 = 144 cm

Perimeters of all nuts and bolts is 48 cm and 144 cm

Question 5: One side is 12 cm long in a hexagon. Find the length of the remaining four sides and find the perimeter.

 In geometry, a hexagon is said to the polygon which has six sides and six angles. Hexa comes from the Greek word “Hex” meaning “six” in English and “gonia” meaning angles. If all the six sides are equal, then it is called a regular hexagon. Naturally, the perimeter of the regular hexagon will be 6 multiplied by one side of the hexagon. Each internal angle of the hexagon is

\(\begin{array}{l}120^{\circ}\end{array} \)

\[\large P=6\times a\]

Where,

a = Length of a side

Solved Example

Question: Find the perimeter of the regular hexagon with one side 12 cm.

Solution:

Given,
a = 12 cm

Formula of hexagon perimeter,

P = 6

\(\begin{array}{l}\times\end{array} \)

P = 6

\(\begin{array}{l}\times\end{array} \)

P = 72 cm

Example 2: The perimeter of a hexagonal chessboard is 54 units. Find the side length of this chessboard.

Solution: The hexagonal chessboard has a perimeter of 54 units.

As we know, the formula for finding the perimeter of a hexagon is given by, P = 6a.

Here, we have to find the side length of the chessboard.

So, by substituting the values in the formula,

54 = 6a

We can write this as,

6a = 54

a  = 54 ÷ 6

a = 9 units

Hence, each side of the hexagonal chessboard is 9 units in length.

Example 3: What is the perimeter of an irregular hexagon with sides 4 cm, 5 cm, 3 cm, 6 cm, 5 cm, 7 cm?

Solution: As we have learned, the perimeter formula for an irregular hexagon is the sum of its sides.

So, P = sum of the side lengths of a hexagon

P = 4 + 5 + 3 + 6 + 5 + 7

P = 30 cm

Hence, the perimeter of the irregular hexagon is 30 cm.

Example 4: Robert purchased a hexagonal prism that has an equal side length of 6 units. Find the perimeter of the hexagonal prism.

Solution: The hexagonal prism has six equal sides of 6 units. According to the perimeter of hexagon formula,

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