Question

The side of a regular polygon is $2.5cm$. If the perimeter of the polygon is $15cm$, then find the number of the sides of the polygon.

Answer 1

Hint:
We will use the definition of the regular polygon to solve for the number of sides of the given polygon as the regular polygon has all sides of equal length. The perimeter of any polygon is the sum of all sides of the polygon so we will equate the perimeter with the sum of the sides by assuming the number of sides to be “$n$ ” i.e. $15 = {\text{ sum of all the sides of the polygon}}$ and we will solve this equation for the value of n.

Complete step by step solution:
We are given a side of a regular polygon as $2.5cm$ and the perimeter of the regular polygon as $15cm$.
We know that a regular polygon is defined as a polygon that has all sides of the same length and all angles are equal as well.
Let the given regular polygon have a total of “$n$” sides.
We are given the perimeter of the polygon as $15cm$ and we can define the perimeter of any polygon as the sum of all sides of a polygon. Since the sides of a regular polygon are equal in length, the perimeter of a regular polygon is defined as: $P = n \times s$ where n is the number of sides and s is the length of any side of the regular polygon.
Here, $s = 2.5cm$ and $P = 15cm$. Using the formula of the perimeter of a regular polygon, we can find the value of n i.e., the number of sides of the given regular polygon.
Using the formula: $P = n \times s$, we get
$
   \Rightarrow P = n \times s \\
   \Rightarrow 15 = n \times 2.5 \\
 $
Solving this equation, for the value of n, we get
$
   \Rightarrow \dfrac{{15cm}}{{2.5cm}} = n \\
   \Rightarrow n = \dfrac{{150}}{{25}} = 6 \\
 $

Hence, the total number of sides is $n = 6$. Therefore, the given regular polygon is a regular hexagon.

Note:
In this question, you may only get confused in the method used as we have used the definition of a regular polygon to deduce the perimeter of the polygon ($P = n \times s$) so as to calculate the number of sides. A regular polygon is generally defined as a polygon which is equilateral (all sides are of same length) and equiangular (all angles are equal).