Question

Which equation can be used to find the perimeter of a regular octagon with sides of length \[12\]?

Answer 1

Hint: In this question, we have to write the equation of the perimeter of the regular octagon. We know that a regular polygon is one whose, all the sides are equal and the perimeter of any polygon is the sum of all sides. So, we have to multiply the side length with the number of sides to find an equation.

Complete step-by-step answer:
In the above question, it is given that the polygon is a regular octagon whose side length is \[12\].
We know that in any regular shape, all the sides are the same length and the perimeter is the sum of all the sides of a polygon.
Also,
For an equilateral triangle: $P\, = \,3 \times side = 3s$
For a square: $P = 4 \times side = 4s$
For a regular octagon there are $8$ equal sides, so
$P = 8 \times side = 8s$
A general formula for the perimeter of a regular figure would be:
$P = n \times side = n \times s$
Where, $n = $ number of sides and $s = $ the length of each side.
In this case
Perimeter $ = \,8 \times 12 = 96$
Therefore, the equation which can be used to find the perimeter of a regular octagon is $P = 8 \times side = 8s$.

Note: In this question, we are dealing with regular polygons. But in the case of irregular polygons there is no such formula. In the case of regular polygons, if we want to find the perimeter, we have to add all the sides individually. We can’t multiply the side length with the number of sides to find the perimeter of such a polygon.