Perimeter and Area | A

Question 3

Find various objects from your surroundings that have regular shapes and find their perimeters. Also, generalise your understanding for the perimeter of other regular polygons.

Solution

Understand the Question

A regular polygon is a closed geometric shape in which all sides are equal in length.
The perimeter of any closed shape is the total distance around its boundary (the sum of all its side lengths).
Because all sides of a regular polygon are equal, finding its perimeter simplifies from repeated addition to multiplication: $\text{Perimeter} = (\text{Number of sides}) \times (\text{Length of one side})$

Step 1 · Perimeter of a Square Table

Consider a square table. A square has $4$ equal sides. Let its side length be $1\text{ m}$ . Diagram 1

\begin{aligned} \text{Perimeter} &= \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} \\[0.6em] &= 1\text{ m} + 1\text{ m} + 1\text{ m} + 1\text{ m} \\[0.6em] &= 4 \times 1\text{ m} \\[0.6em] &= 4\text{ m} \end{aligned}

Step 2 · Perimeter of an Equilateral Triangular Clock

Consider a wall clock shaped as an equilateral triangle. An equilateral triangle has $3$ equal sides. Let its side length be $30\text{ cm}$ . Diagram 2

\begin{aligned} \text{Perimeter} &= \text{Side length} + \text{Side length} + \text{Side length} \\[0.6em] &= 30\text{ cm} + 30\text{ cm} + 30\text{ cm} \\[0.6em] &= 3 \times 30\text{ cm} \\[0.6em] &= 90\text{ cm} \end{aligned}

Step 3 · Perimeter of a Regular Hexagonal Tile

Consider a floor tile shaped as a regular hexagon. A regular hexagon has $6$ equal sides. Let its side length be $10\text{ cm}$ .$$ \begin{aligned} \text{Perimeter} &= \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} \[0.6em] &= 10\text{ cm} + 10\text{ cm} + 10\text{ cm} + 10\text{ cm} + 10\text{ cm} + 10\text{ cm} \[0.6em] &= 6 \times 10\text{ cm} \[0.6em] &= 60\text{ cm} \end{aligned}

Step 4 · Generalisation for Any Regular Polygon

For any regular polygon, every side has the exact same length. Let $n$ be the number of sides and $s$ be the length of one side.

$\text{Perimeter of a Regular Polygon} = \text{Number of sides} \times \text{Side length}$

$\text{Perimeter} = n \times s$

Answer

$\text{Perimeter of a Regular Polygon} = (\text{Number of sides}) \times (\text{Side length of the polygon})$

Common Mistakes

Applying to Irregular Shapes: The formula $\text{Perimeter} = n \times s$ only applies when all side lengths are equal (regular polygons). If side lengths differ, you must add each side individually.
Confusing Perimeter with Area: Perimeter measures the outer boundary length in linear units ( $\text{cm}$ , $\text{m}$ ), not surface area in square units ( $\text{cm}^2$ , $\text{m}^2$ ).

Question 3

More questions in A