Introduction to Area
Area is the amount of surface a shape covers. When you paint a wall or lay tiles on a floor, you are covering an area.
In Class 4, you will learn what area means, how to measure area by counting square units, and how area differs from perimeter.
What is Introduction to Area - Class 4 Maths (Measurement)?
Area is the measure of the surface enclosed inside a closed shape. It tells you how much space the shape covers on a flat surface.
Area is measured in square units:
- Square centimetre (sq cm or cm²) — the area of a square with side 1 cm.
- Square metre (sq m or m²) — the area of a square with side 1 m.
Introduction to Area Formula
Area = Number of unit squares that fit inside the shape
To find the area of a shape drawn on a grid, count the number of complete squares inside the shape. For half squares, count two halves as one full square.
Types and Properties
Methods to find area:
- Counting squares: Draw the shape on a grid and count the squares it covers.
- Using a formula: For rectangles and squares, use length × breadth or side × side (covered in detail in the next topics).
Area vs Perimeter:
| Area | Perimeter |
|---|---|
| Space inside a shape | Distance around a shape |
| Measured in sq cm, sq m | Measured in cm, m |
| Used for painting, tiling | Used for fencing, bordering |
Solved Examples
Example 1: Example 1: Counting squares
Problem: A rectangle on a grid covers 3 columns and 4 rows of unit squares. Find its area.
Solution:
Step 1: Count the unit squares: 3 × 4 = 12 squares.
Answer: The area is 12 sq cm.
Example 2: Example 2: Area of a square on a grid
Problem: A square on a grid covers 5 rows and 5 columns. Find its area.
Solution:
Step 1: Count: 5 × 5 = 25 unit squares.
Answer: The area is 25 sq cm.
Example 3: Example 3: Counting with half squares
Problem: A shape on a grid covers 10 full squares and 4 half squares. What is the area?
Solution:
Step 1: Full squares = 10.
Step 2: Half squares = 4 halves = 4 ÷ 2 = 2 full squares.
Step 3: Total area = 10 + 2 = 12 sq cm.
Answer: The area is 12 sq cm.
Example 4: Example 4: Comparing areas
Problem: Shape A covers 15 unit squares. Shape B covers 12 unit squares. Which has a larger area?
Solution:
Step 1: Area of A = 15 sq cm. Area of B = 12 sq cm.
Step 2: 15 > 12.
Answer: Shape A has a larger area by 3 sq cm.
Example 5: Example 5: Area of your palm
Problem: Ria places her hand on a grid paper. Her palm covers 18 full squares and 6 half squares. What is the approximate area?
Solution:
Step 1: Full squares = 18.
Step 2: Half squares = 6 ÷ 2 = 3.
Step 3: Total = 18 + 3 = 21 sq cm.
Answer: The area of Ria's palm is approximately 21 sq cm.
Example 6: Example 6: Area vs perimeter
Problem: A rectangle is 6 cm long and 2 cm wide. Find both its area and perimeter.
Solution:
Step 1: Area = Length × Breadth = 6 × 2 = 12 sq cm.
Step 2: Perimeter = 2 × (6 + 2) = 2 × 8 = 16 cm.
Answer: Area = 12 sq cm. Perimeter = 16 cm. (Notice: area uses square units, perimeter uses linear units.)
Example 7: Example 7: Same perimeter, different area
Problem: Shape A is 4 cm × 4 cm. Shape B is 6 cm × 2 cm. Both have the same perimeter (16 cm). Do they have the same area?
Solution:
Step 1: Area of A = 4 × 4 = 16 sq cm.
Step 2: Area of B = 6 × 2 = 12 sq cm.
Step 3: 16 ≠ 12.
Answer: No. Even though both shapes have the same perimeter, the square has a larger area (16 sq cm) than the rectangle (12 sq cm).
Example 8: Example 8: L-shaped figure
Problem: An L-shaped figure is drawn on a grid. Count: 20 full squares are inside the shape. What is the area?
Solution:
Step 1: Count all unit squares inside the boundary: 20.
Answer: The area of the L-shape is 20 sq cm.
Example 9: Example 9: Tiling a floor
Problem: Kavi wants to cover a rectangular table top with square tiles. The table is 8 tiles long and 5 tiles wide. How many tiles does he need?
Solution:
Step 1: Number of tiles = 8 × 5 = 40.
Answer: Kavi needs 40 tiles to cover the table.
Real-World Applications
Understanding area is useful for:
- Painting — to know how much paint to buy for a wall.
- Flooring — to know how many tiles are needed for a room.
- Gardening — to calculate how much grass seed for a lawn.
- Crafts — to cut the right amount of paper or cloth.
Key Points to Remember
- Area is the surface enclosed inside a shape.
- It is measured in square units (sq cm, sq m).
- To find area on a grid, count the unit squares.
- Two halves = one full square.
- Area measures space inside; perimeter measures distance around.
- Shapes with the same perimeter can have different areas.
- Shapes with the same area can have different perimeters.
Practice Problems
- Draw a rectangle on grid paper that is 7 units long and 3 units wide. Count the squares to find the area.
- A shape covers 14 full squares and 8 half squares on a grid. What is its area?
- Which has a bigger area: a 5 cm × 5 cm square or a 7 cm × 3 cm rectangle?
- Aman says two shapes with the same perimeter always have the same area. Is he correct? Show an example.
- Place your maths textbook on grid paper and trace around it. Count the squares to estimate its area.
- A rectangular floor is 10 tiles long and 8 tiles wide. How many tiles cover the floor?
- Draw two different shapes on grid paper that each have an area of 12 sq cm.
Frequently Asked Questions
Q1. What is area in maths?
Area is the amount of surface enclosed inside a flat shape. It measures how much space the shape covers and is expressed in square units like sq cm or sq m.
Q2. How do you find the area of a shape on a grid?
Count the number of complete unit squares inside the shape. For partial squares, count two half-squares as one full square.
Q3. What is the difference between area and perimeter?
Area measures the space inside a shape (in square units). Perimeter measures the distance around the boundary (in linear units like cm or m).
Q4. What are square units?
Square units measure area. One square centimetre (sq cm) is the area of a square with side 1 cm. One square metre (sq m) is the area of a square with side 1 m.
Q5. Can two shapes have the same area but different perimeters?
Yes. A 4 × 3 rectangle (area 12 sq cm, perimeter 14 cm) and a 6 × 2 rectangle (area 12 sq cm, perimeter 16 cm) have the same area but different perimeters.
Q6. Why is area measured in square units and not just cm?
Area measures a surface (two-dimensional), so it needs two measurements multiplied together. The result is in 'squared' units. Perimeter measures a line (one-dimensional), so it uses plain cm or m.
Q7. How do you handle partial squares when counting area?
Count each half-square as 0.5. Add up the halves — two halves make one full square. Ignore very small slivers if they are less than half a square.
Q8. What is the area of a 1 cm × 1 cm square?
Exactly 1 square centimetre (1 sq cm or 1 cm²). This is the basic unit used to measure area on a grid.
Related Topics
- Area of Rectangle (Grade 4)
- Perimeter (Grade 4)
- Area of Square (Grade 4)
- Area and Perimeter Word Problems (Grade 4)
- Converting Units of Length (Grade 4)
- Converting Units of Weight (Grade 4)
- Converting Units of Capacity (Grade 4)
- Area by Counting Squares
- Perimeter of Irregular Shapes
- Relationship Between Area and Perimeter
