Chapter 7: The Cleanest Village

Mawlynnong in Meghalaya is called the cleanest village in Asia. Tidy houses, swept lanes, gardens. Let's measure those gardens , using area and perimeter.

What we'll learn

• The difference between area and perimeter.
• How to measure perimeter by adding sides.
• How to count squares to find area.
• Compare shapes by their area and perimeter.

The big idea

Perimeter is the distance around a shape. If you walk along the edge of a garden and come back, the total length is its perimeter. For a rectangle, just add all 4 sides.

Area is the space inside a shape. Think of it as how much carpet you need to cover the floor. We measure area in square units , like square cm, square m.

A square of side 1 cm is called 1 sq cm. Place this small square inside a bigger shape and count how many fit. That count is the area.

For a rectangle with length 5 cm and width 3 cm, the area = 5 × 3 = 15 sq cm. Length times width gives area for any rectangle.

Two shapes can have the same area but different perimeters. A long thin rectangle uses more fence than a fat square with the same area.

Explore with examples

1. A rectangular garden is 6 m long and 4 m wide. Find its perimeter.

Perimeter = 6 + 4 + 6 + 4 = 20 m.

2. Find the area of the same garden.

Area = 6 × 4 = 24 sq m.

3. A square room has side 5 m. Find its area and perimeter.

Perimeter = 4 × 5 = 20 m. Area = 5 × 5 = 25 sq m.

4. Compare two rectangles: one 2 cm × 6 cm, another 3 cm × 4 cm.

• Area first: 2 × 6 = 12, 3 × 4 = 12. Same area!
• Perimeter: 2 + 6 + 2 + 6 = 16, 3 + 4 + 3 + 4 = 14.
• The 3 × 4 shape needs less fencing.

Hands-on activities

Newspaper Carpet

Spread newspaper sheets on your room floor. Count how many sheets cover the floor with no gaps. That count gives the area of your floor in "newspaper units".

Garden Walk

Step around the edge of a flowerbed at home or school. Count your steps. That is its perimeter in step-units.

Graph Paper Maps

On square graph paper, draw any closed shape. Count squares inside to find area. Count the boundary unit-lengths to find perimeter.

Try it yourself

1. A rectangle is 8 cm long, 5 cm wide. Perimeter? Area?
2. A square has side 7 m. Find perimeter and area.
3. A field has 4 sides: 12 m, 9 m, 12 m, 9 m. Perimeter?
4. Draw two shapes both with area 16 sq cm but different perimeters.
5. To put a fence around a square garden of side 10 m, how many metres of fence?
6. The classroom floor is 8 m × 6 m. How many 1 m × 1 m tiles to cover it?
7. Which has more area: a 5 × 5 square or a 4 × 6 rectangle?

Recap

• Perimeter = distance around. Add all sides.
• Area = space inside. For rectangles, length × width.
• Same area can give different perimeters.
• Measure area in square units (sq cm, sq m).