Question 3

We will find the distance around some regular shapes.

Step 1 — Square Table Perimeter

Let us look at a square table. A square has 4 equal sides. Let its side length be 1 meter. We add all side lengths to find the perimeter.

$\text{Perimeter} = \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length}$

$= 1 \text{ m} + 1 \text{ m} + 1 \text{ m} + 1 \text{ m}$

$= 4 \times 1 \text{ m}$

$\boxed{4 \text{ m}}$

Step 2 — Equilateral Triangle Clock Perimeter

Let us look at an equilateral triangle clock. An equilateral triangle has 3 equal sides. Let its side length be 30 centimeters. We add all side lengths to find the perimeter.

$\text{Perimeter} = \text{Side length} + \text{Side length} + \text{Side length}$

$= 30 \text{ cm} + 30 \text{ cm} + 30 \text{ cm}$

$= 3 \times 30 \text{ cm}$

$\boxed{90 \text{ cm}}$

Step 3 — Hexagonal Tile Perimeter

Let us look at a hexagonal tile. A regular hexagon has 6 equal sides. Let its side length be 10 centimeters. We add all side lengths to find the perimeter.

$\text{Perimeter} = \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length} + \text{Side length}$

$= 10 \text{ cm} + 10 \text{ cm} + 10 \text{ cm} + 10 \text{ cm} + 10 \text{ cm} + 10 \text{ cm}$

$= 6 \times 10 \text{ cm}$

$\boxed{60 \text{ cm}}$

Step 4 — Generalization for Regular Polygons

We saw that for a square, we multiplied the side length by 4. For an equilateral triangle, we multiplied the side length by 3. For a regular hexagon, we multiplied the side length by 6. The number we multiply by is always the number of sides. This works for any regular polygon. A regular polygon has all sides equal. Let 'n' be the number of sides. Let 's' be the length of one side. The perimeter is 'n' times 's'.

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

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

Answer

(i) Examples of regular shapes in surroundings:

1. Square Table: Shape: Square, Side Length = 1 m, Perimeter = 4 m
2. Equilateral Triangle Clock: Shape: Equilateral Triangle, Side Length = 30 cm, Perimeter = 90 cm
3. Hexagonal Tile: Shape: Regular Hexagon, Side Length = 10 cm, Perimeter = 60 cm (ii) Generalization: Perimeter of a Regular Polygon = (Number of sides) * (Side length of the polygon) units.