Area of Square (Grade 4)
A square is a rectangle with all four sides equal. Finding the area of a square is straightforward — multiply the side by itself.
In Class 4, you will learn the formula for the area of a square, solve word problems involving square areas, and find the side when the area is known.
What is Area of Square - Class 4 Maths (Measurement)?
The area of a square is the space enclosed within its four equal sides. Since all sides are the same length, you multiply the side by itself.
Area of Square (Grade 4) Formula
Area of Square = Side × Side
This is often written as s × s or s² (s squared).
To find the side when area is known: Side = the number whose square is the area. For example, if area = 49 sq cm, then side = 7 cm (because 7 × 7 = 49).
Solved Examples
Example 1: Example 1: Basic area calculation
Problem: Find the area of a square with side 8 cm.
Solution:
Step 1: Area = Side × Side = 8 × 8 = 64 sq cm
Answer: The area is 64 sq cm.
Example 2: Example 2: Square tile
Problem: A square tile has a side of 15 cm. Find its area.
Solution:
Step 1: Area = 15 × 15 = 225 sq cm
Answer: The area of the tile is 225 sq cm.
Example 3: Example 3: Finding the side from area
Problem: The area of a square garden is 81 sq m. Find the side.
Solution:
Step 1: Side × Side = 81
Step 2: 9 × 9 = 81
Answer: The side of the garden is 9 m.
Example 4: Example 4: Cloth for a square table
Problem: Aditi wants to cover a square table with a side of 90 cm using cloth. How much cloth does she need?
Solution:
Step 1: Area = 90 × 90 = 8,100 sq cm
Answer: Aditi needs 8,100 sq cm of cloth.
Example 5: Example 5: Comparing a square and a rectangle
Problem: A square has side 6 cm. A rectangle has length 9 cm and breadth 4 cm. Which has a larger area?
Solution:
Step 1: Area of square = 6 × 6 = 36 sq cm
Step 2: Area of rectangle = 9 × 4 = 36 sq cm
Answer: Both have the same area: 36 sq cm.
Example 6: Example 6: Perimeter and area of a square
Problem: A square has a perimeter of 48 cm. Find its area.
Solution:
Step 1: Side = Perimeter ÷ 4 = 48 ÷ 4 = 12 cm
Step 2: Area = 12 × 12 = 144 sq cm
Answer: The area is 144 sq cm.
Example 7: Example 7: Painting cost
Problem: Rahul wants to paint a square wall with side 4 m. Paint costs ₹25 per sq m. What is the total cost?
Solution:
Step 1: Area = 4 × 4 = 16 sq m
Step 2: Cost = 16 × ₹25 = ₹400
Answer: The painting cost is ₹400.
Example 8: Example 8: Number of tiles
Problem: A square floor has side 6 m. Each square tile has side 1 m. How many tiles are needed?
Solution:
Step 1: Area of floor = 6 × 6 = 36 sq m
Step 2: Area of each tile = 1 × 1 = 1 sq m
Step 3: Number of tiles = 36 ÷ 1 = 36
Answer: 36 tiles are needed.
Example 9: Example 9: Square photo frame
Problem: A square photo is 20 cm on each side. A border 2 cm wide is added around it. Find the area of the border.
Solution:
Step 1: Outer side = 20 + 2 + 2 = 24 cm (border on both sides)
Step 2: Outer area = 24 × 24 = 576 sq cm
Step 3: Inner area (photo) = 20 × 20 = 400 sq cm
Step 4: Border area = 576 − 400 = 176 sq cm
Answer: The area of the border is 176 sq cm.
Key Points to Remember
- Area of Square = Side × Side (or s²).
- Area is measured in square units (sq cm, sq m).
- To find the side from area, ask: what number multiplied by itself gives the area?
- If you know the perimeter, find the side first (side = perimeter ÷ 4), then calculate area.
- A square is a special rectangle, so the rectangle area formula also works (l × b where l = b).
- Always include the correct unit in your answer.
Practice Problems
- Find the area of a square with side 11 cm.
- A square garden has area 100 sq m. What is the length of each side?
- A square handkerchief has side 25 cm. Find its area.
- The perimeter of a square is 60 cm. Find its area.
- Dev has a square piece of land with side 40 m. He sells half of it. What area did he sell?
- How many 1 cm × 1 cm stamps can fit on a square card of side 10 cm?
- A square painting is 50 cm on each side. A frame 3 cm wide is placed around it. Find the total area including the frame.
Frequently Asked Questions
Q1. What is the formula for the area of a square?
Area of a square = Side × Side. For a square with side 5 cm, area = 5 × 5 = 25 sq cm.
Q2. How do you find the side of a square if the area is given?
Find the number that when multiplied by itself gives the area. If area = 64 sq cm, the side = 8 cm because 8 × 8 = 64.
Q3. What is the difference between area and perimeter of a square?
Area = side × side (in sq cm). Perimeter = 4 × side (in cm). Area measures the surface inside; perimeter measures the distance around.
Q4. Is a square also a rectangle?
Yes. A square is a special rectangle where all four sides are equal. The formula Area = length × breadth still works — with length = breadth = side.
Q5. Can the area and perimeter of a square be equal?
Numerically, yes — for a square with side 4 units: area = 16 square units and perimeter = 16 units. But they have different units, so the comparison is only numerical.
Q6. What is the area of a 1 cm × 1 cm square?
Exactly 1 sq cm (1 cm²). This is the basic unit square used to measure area.
Q7. How many small squares fit inside a larger square?
Divide the area of the large square by the area of the small square. For a 10 cm square filled with 2 cm squares: 100 ÷ 4 = 25 small squares.
Q8. What is 'squared' in maths?
A number 'squared' means the number multiplied by itself. 5 squared = 5 × 5 = 25. It comes from the area of a square — a square with side 5 has area 25.
Related Topics
- Area of Rectangle (Grade 4)
- Introduction to Area
- Perimeter (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
