Area by Counting Squares
Before learning formulas for area, you can find the area of a shape by counting the squares it covers on a grid. This method gives a hands-on understanding of what area really means — the amount of flat surface a shape covers.
In Class 4, you use grid paper (squared paper) to find the area of regular and irregular shapes by counting the number of unit squares inside the shape.
What is Area by Counting Squares - Class 4 Maths (Measurement)?
Area is the amount of surface enclosed by a shape. It is measured in square units (sq cm, sq m, etc.).
Area = Number of unit squares covered by the shape
Rules for counting squares:
- Full squares: Count each full square as 1.
- Half squares (or more than half): Count each as 1.
- Less than half squares: Count as 0 (ignore).
- Exactly half: Count as 1/2 (or count two halves as 1).
Solved Examples
Example 1: Example 1: Rectangle on Grid
Problem: A rectangle on a grid covers 4 columns and 3 rows of squares. Find its area.
Solution:
Step 1: Count full squares: 4 x 3 = 12
Answer: Area = 12 square units
Example 2: Example 2: Square on Grid
Problem: A square covers 5 rows and 5 columns on a grid. Find its area.
Solution:
Full squares = 5 x 5 = 25
Answer: Area = 25 square units
Example 3: Example 3: L-shaped Figure
Problem: An L-shaped figure on a grid has 14 full squares. Find its area.
Solution:
Count all the full squares inside the L-shape: 14.
Answer: Area = 14 square units
Example 4: Example 4: Shape with Half Squares
Problem: A triangle on a grid covers 6 full squares and 4 half squares. Find the area.
Solution:
Step 1: Full squares = 6
Step 2: Half squares = 4 halves = 4 x 1/2 = 2
Step 3: Total area = 6 + 2 = 8
Answer: Area = 8 square units
Example 5: Example 5: Irregular Shape
Problem: An irregular shape on a grid covers 10 full squares, 6 more-than-half squares, and 3 less-than-half squares. Estimate the area.
Solution:
Step 1: Full squares = 10 (count as 10)
Step 2: More-than-half squares = 6 (count as 6)
Step 3: Less-than-half squares = 3 (count as 0)
Step 4: Estimated area = 10 + 6 + 0 = 16
Answer: Area ≈ 16 square units
Example 6: Example 6: Comparing Areas
Problem: Shape A covers 18 squares on a grid. Shape B covers 15 squares. Which has a greater area?
Solution:
18 > 15
Answer: Shape A has a greater area.
Example 7: Example 7: Word Problem — Handkerchief
Problem: Ria places a handkerchief on grid paper. It covers 9 full squares and 2 half squares. What is its area?
Solution:
Area = 9 + 2 x (1/2) = 9 + 1 = 10
Answer: Area = 10 square units
Example 8: Example 8: Drawing a Shape of Given Area
Problem: On a grid, draw a shape with an area of 12 square units.
Solution:
Draw a rectangle that is 4 squares long and 3 squares wide. Count: 4 x 3 = 12. Other shapes like L-shapes or T-shapes covering 12 squares also work.
Answer: Any shape covering exactly 12 full squares.
Example 9: Example 9: Leaf on a Grid
Problem: A leaf placed on grid paper covers 7 full squares, 5 more-than-half squares, and 4 less-than-half squares. Estimate the area.
Solution:
Area ≈ 7 + 5 + 0 = 12
Answer: Area ≈ 12 square units
Key Points to Remember
- Area = number of square units covered by a shape.
- On a grid, count full squares as 1, more-than-half as 1, less-than-half as 0.
- Two half squares together count as 1 square unit.
- The counting method works for regular and irregular shapes.
- Area is measured in square units (sq cm, sq m).
- Different shapes can have the same area but look very different.
Practice Problems
- A rectangle on a grid is 6 squares long and 4 squares wide. Find its area by counting.
- A shape on grid paper covers 15 full squares and 6 half squares. Find the area.
- An irregular shape covers 8 full squares, 4 more-than-half, and 5 less-than-half. Estimate the area.
- Draw two different shapes on grid paper, each with an area of 10 square units.
- Kavi placed his palm on grid paper. It covered 22 full squares and 8 half squares. What is the approximate area?
- A triangle on a grid covers 3 full squares and 6 half squares. Find the area.
- Which has more area: a shape covering 20 full squares or one covering 18 full squares and 6 half squares?
Frequently Asked Questions
Q1. How do you find area by counting squares?
Place the shape on a grid and count the number of squares it covers. Full squares count as 1. More-than-half squares also count as 1. Less-than-half squares are ignored.
Q2. What is a square unit?
A square unit is a square with sides of 1 unit length. If each grid square has sides of 1 cm, the area is in square centimetres (sq cm).
Q3. How do you handle partial squares?
Count more-than-half squares as 1 full unit. Count less-than-half squares as 0. For exactly half squares, count two halves as 1.
Q4. Can two shapes have the same area but different shapes?
Yes. A 3x4 rectangle and a 2x6 rectangle both have 12 square units of area but look different. Even L-shapes and T-shapes can have 12 square units.
Q5. Is this method only for rectangles?
No. Counting squares works for any shape — triangles, circles, irregular shapes, even leaf shapes. It is especially useful for shapes that do not have a formula.
Q6. Why learn counting squares when there are formulas?
Counting squares builds an intuitive understanding of what area means before learning formulas. It also works for irregular shapes where no formula exists.
Q7. What is the difference between area and perimeter?
Area is the surface covered (measured in square units). Perimeter is the distance around the boundary (measured in linear units like cm or m).
Q8. Is area by counting squares part of NCERT Class 4?
Yes, finding area by counting squares on a grid is part of the CBSE/NCERT Class 4 Maths curriculum under the Measurement chapter.
Related Topics
- Introduction to Area
- 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)
- Perimeter of Irregular Shapes
- Relationship Between Area and Perimeter
