Area , the covering
Area is how much flat space a shape covers. If you spread a chatai (mat) on the floor, the area of the chatai tells you how much floor it covers.
What is this?
Area is measured in square units , square centimetres (sq cm), square metres (sq m), and so on. One square centimetre is the area of a tiny square with each side 1 cm.
To find the area of any rectangle or square, we count how many such squares fit inside.
For a rectangle with length 5 cm and breadth 3 cm, we can draw a grid of 5 across and 3 down. That gives us 5 × 3 = 15 squares. So the area is 15 sq cm.
The rule is:
For a square with side :
So a square of side 4 m has area 4 × 4 = 16 sq m.
Area and perimeter are different things, even though both are about shapes. Perimeter is the boundary (a length). Area is the inside (a covering).
Two shapes can have the same perimeter but different areas. A 1 × 5 rectangle has perimeter 12 and area 5. A 2 × 4 rectangle has perimeter 12 and area 8. A 3 × 3 square has perimeter 12 and area 9. Same perimeter, bigger area as the shape becomes square-ish.
Worked examples
Example 1. A rectangular plot is 25 m long and 12 m wide. Area?
- 25 × 12 = 300 sq m.
Example 2. A square tile has side 30 cm. Area?
- 30 × 30 = 900 sq cm.
Example 3. A room is 6 m × 4 m. How many 1 sq m tiles cover the floor?
- Area = 6 × 4 = 24 sq m.
- Tiles needed = 24.
Try it
- Rectangle: 8 cm × 5 cm. Area?
- Square: side 7 m. Area?
- A field is 50 m × 30 m. Area?
- A floor is 5 m × 4 m. If each tile is 1 sq m, how many tiles?
- A square plot has area 64 sq m. Find one side.
Hands-on
Grid count. On a square-ruled paper, draw any rectangle. Count the small squares inside. That is the area. Verify by multiplying length × breadth.
Floor tile count. Pick a small rectangular area of tile floor. Count the tiles along one side and along the other side. Multiply them. That is the floor area in "tile units".