Question

The perimeter of a regular octagon is 53.6 cm. Find the length of each side.

Answer 1

Hint – In this question use the concept that a regular octagon has eight equal sides, so let the sides be x cm, then simply use the concept that perimeter is the sum of all sides. This will help getting the value of the side of a regular octagon.
Complete step-by-step answer:

A regular octagon ABCDEFGH is shown above.
Given data:
Perimeter of a regular octagon is 53.6 cm
As we know that the perimeter of any shape is the sum of all the sides.
Now as we know that a regular octagon has 8 equal sides as shown in the figure.
So let the length of any side be x cm.
So the sum of all the sides of the octagon = perimeter of the octagon
$ \Rightarrow x + x + x + x + x + x + x + x = 53.6$
$ \Rightarrow 8x = 53.6$
Now divide by 8 we have,
$ \Rightarrow x = \dfrac{{53.6}}{8} = 6.7$ cm.
So this is the required length of each side of a regular octagon.
So this is the required answer.

Note – An octagon is an 8-sided polygon. One important information about a regular octagon is that it has a total 20 diagonals, and each exterior angle of the octagon is ${45^0}$. Using the property that angles opposite to equal sides are equal we can also say that all the angles should be equal, as all the sides of a regular octagon are equal.