Area (Grade 5)
Area is the amount of surface a flat shape covers. When you paint a wall, the paint covers the area of the wall. When you tile a floor, the tiles cover the area of the floor.
Area is different from perimeter. Perimeter measures the boundary (how far you walk around the shape), while area measures the surface (how much paint or carpet you need to cover it).
In Class 5, you will learn to calculate the area of rectangles, squares, and composite shapes using formulas and by counting square units. You will also solve real-life problems involving flooring, painting, tiling, and land measurement.
What is Area - Class 5 Maths (Measurement)?
The area of a closed figure is the measure of the surface enclosed within its boundary. Area is measured in square units (sq cm, sq m, etc.).
One square centimetre (1 sq cm or 1 cm²) is the area of a square with side 1 cm.
Area (Grade 5) Formula
Area of Rectangle = Length × Breadth
Area of Square = Side × Side = Side²
Unit conversions:
- 1 m² = 10,000 cm²
- 1 km² = 1,000,000 m²
- 1 hectare = 10,000 m²
Types and Properties
Methods to Find Area:
- Using formulas: Apply the area formula for rectangles and squares directly.
- Counting squares: Draw the shape on grid paper and count the unit squares inside. Count full squares, then half squares (two halves = one full).
- Splitting composite shapes: Break an irregular shape into rectangles and squares, find the area of each part, and add them together.
Solved Examples
Example 1: Example 1: Area of a Rectangle
Problem: Find the area of a rectangle with length 12 cm and breadth 7 cm.
Solution:
Step 1: Area = Length × Breadth
Step 2: Area = 12 × 7 = 84 cm²
Answer: The area is 84 cm².
Example 2: Example 2: Area of a Square
Problem: A square tile has a side of 15 cm. Find its area.
Solution:
Step 1: Area = Side × Side
Step 2: Area = 15 × 15 = 225 cm²
Answer: The area is 225 cm².
Example 3: Example 3: Finding a Missing Dimension
Problem: A rectangle has area 96 cm² and length 12 cm. Find the breadth.
Solution:
Step 1: Area = Length × Breadth
Step 2: 96 = 12 × Breadth
Step 3: Breadth = 96 ÷ 12 = 8 cm
Answer: The breadth is 8 cm.
Example 4: Example 4: Tiling a Floor
Problem: Ria’s room is 5 m long and 4 m wide. She wants to tile it with square tiles of side 50 cm. How many tiles does she need?
Solution:
Step 1: Room area = 5 × 4 = 20 m² = 200,000 cm²
Step 2: Tile area = 50 × 50 = 2,500 cm²
Step 3: Number of tiles = 200,000 ÷ 2,500 = 80
Answer: Ria needs 80 tiles.
Example 5: Example 5: Cost of Painting
Problem: A wall is 8 m long and 3 m high. Painting costs ₹25 per sq m. Find the total cost.
Solution:
Step 1: Area = 8 × 3 = 24 m²
Step 2: Cost = 24 × 25 = ₹600
Answer: The total cost is ₹600.
Example 6: Example 6: Area of an L-Shaped Figure
Problem: An L-shaped room can be split into two rectangles: one is 6 m × 3 m and the other is 4 m × 2 m. Find the total area.
Solution:
Step 1: Area of Rectangle 1 = 6 × 3 = 18 m²
Step 2: Area of Rectangle 2 = 4 × 2 = 8 m²
Step 3: Total area = 18 + 8 = 26 m²
Answer: The total area is 26 m².
Example 7: Example 7: Finding Side from Area (Square)
Problem: A square has an area of 144 cm². Find its side.
Solution:
Step 1: Area = Side × Side
Step 2: Side × Side = 144
Step 3: Side = √144 = 12 cm
Answer: The side is 12 cm.
Example 8: Example 8: Comparing Areas
Problem: Which has more area: a square of side 9 cm or a rectangle of 10 cm × 8 cm?
Solution:
Step 1: Area of square = 9 × 9 = 81 cm²
Step 2: Area of rectangle = 10 × 8 = 80 cm²
Step 3: 81 > 80
Answer: The square has more area (by 1 cm²).
Example 9: Example 9: Area with Unit Conversion
Problem: A garden is 50 m long and 30 m wide. Express its area in hectares.
Solution:
Step 1: Area = 50 × 30 = 1,500 m²
Step 2: 1 hectare = 10,000 m²
Step 3: Area = 1,500 ÷ 10,000 = 0.15 hectares
Answer: The area is 0.15 hectares.
Example 10: Example 10: Area by Counting Squares
Problem: A shape drawn on grid paper covers 14 full squares and 6 half squares. What is its area?
Solution:
Step 1: Full squares contribute 14 sq units.
Step 2: Half squares: 6 halves = 3 full squares.
Step 3: Total area = 14 + 3 = 17 sq units.
Answer: The area is 17 square units.
Real-World Applications
Where do we use area?
- Flooring: Calculating how many tiles or how much carpet is needed for a room. Tile shops calculate area to give accurate quotes.
- Painting: Finding the amount of paint for a wall or ceiling. One litre of paint typically covers 10-12 m².
- Farming: Measuring land area for crops, irrigation planning, and fertiliser calculation. Farmers measure fields in hectares or acres.
- Construction: Planning room sizes, plot areas, roofing material, and concrete requirements.
- Wrapping gifts: Calculating how much wrapping paper is needed to cover a box.
- Sports fields: A cricket pitch is 20.12 m × 3.05 m. A football field is approximately 100 m × 64 m. These are area measurements.
- Solar panels: The area of a rooftop determines how many solar panels can be installed.
Key Points to Remember
- Area measures the surface enclosed by a shape.
- Area of rectangle = length × breadth.
- Area of square = side × side.
- Area is measured in square units (cm², m², km²).
- For composite shapes, split into rectangles, find each area, and add.
- On grid paper, count full squares and combine half squares.
- 1 m² = 10,000 cm². 1 hectare = 10,000 m².
- Area and perimeter are different: area measures surface, perimeter measures boundary length.
Practice Problems
- Find the area of a rectangle with length 18 cm and breadth 11 cm.
- A square has a side of 25 m. Find its area.
- A rectangle has area 120 cm² and breadth 10 cm. Find the length.
- Rahul’s classroom is 8 m × 6 m. Find the area in square metres.
- Which is larger: a square of side 7 cm or a rectangle of 8 cm × 6 cm?
- An L-shaped figure is made of two rectangles: 10 cm × 4 cm and 6 cm × 3 cm. Find the total area.
- A rectangular field has area 2 hectares. It is 200 m long. Find its breadth.
- Aditi draws a shape on grid paper. It covers 20 full squares and 4 half squares. What is the area?
Frequently Asked Questions
Q1. What is area in maths?
Area is the measure of the surface enclosed within the boundary of a flat (2D) shape. It tells us how much space the shape covers.
Q2. What is the formula for the area of a rectangle?
Area of a rectangle = length × breadth. Both length and breadth must be in the same unit.
Q3. What is the difference between area and perimeter?
Area measures the surface inside a shape (in square units). Perimeter measures the total length of the boundary (in linear units). A shape can have a large area but small perimeter, or vice versa.
Q4. What are square units?
Square units measure area. One square centimetre (cm²) is the area of a 1 cm × 1 cm square. One square metre (m²) is the area of a 1 m × 1 m square.
Q5. How do you find the area of an irregular shape?
Split the shape into regular shapes (rectangles, squares, triangles), calculate each area separately, then add them together. On grid paper, count full and partial squares.
Q6. How do you find a missing dimension if area is given?
Divide the area by the known dimension. For a rectangle: breadth = area ÷ length. For a square: side = square root of area.
Q7. What is a hectare?
A hectare is a unit of area used for measuring land. 1 hectare = 10,000 m². A square field of 100 m × 100 m = 1 hectare.
Q8. Can two shapes with the same perimeter have different areas?
Yes. For example, a 10×10 square (perimeter 40, area 100) and a 15×5 rectangle (perimeter 40, area 75) have the same perimeter but different areas.
Q9. Why is area measured in square units and not just cm?
Area is two-dimensional — it covers a surface in two directions (length and width). Square units account for both dimensions. Perimeter (one-dimensional) is measured in just cm or m.
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Area of rectangles, squares, and composite shapes is part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
