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.

Solution

We know that,

Sides are equal in hexagon. So all sides are 12 cm

Hence perimeter is 6*s => 6*12 = 72 cm

Therefore the length of remaining four sides are 12 cm each and the perimeter is 72 cm.