Area Word Problems (Grade 5)
Area word problems require you to apply area formulas to real-life situations. Instead of simply calculating length × breadth, you must read the problem, identify the shape, pick the correct formula, and solve step by step.
In Class 5, area word problems involve rectangles, squares, and composite shapes. Common scenarios include tiling floors, painting walls, fencing gardens, and comparing land areas. These problems test both your arithmetic and your ability to understand what the question is asking.
Always check the units. If the length is in metres and the breadth is in centimetres, convert them to the same unit before multiplying.
What is Area Word Problems - Class 5 Maths (Measurement)?
An area word problem is a question that describes a real-life situation and asks you to find the area (or a related measurement) of a shape. You need to extract the dimensions from the words, choose the right formula, and calculate.
Key formulas used:
- Area of rectangle = length × breadth
- Area of square = side × side
- Number of tiles = total area ÷ area of one tile
- Cost = area × rate per square unit
Area Word Problems (Grade 5) Formula
Area of Rectangle = Length × Breadth
Area of Square = Side × Side
Number of tiles = Floor area ÷ Tile area
Types and Properties
Common types of area word problems:
- Tiling/flooring: How many tiles are needed to cover a floor?
- Painting/whitewashing: What is the cost of painting a wall at a given rate per sq m?
- Cost of land: What is the cost of a plot at ₹X per sq m?
- Comparing areas: Which shape or room has a greater area?
- Finding missing dimensions: Given area and one side, find the other side.
- Composite shapes: Find the area of L-shaped, T-shaped, or U-shaped figures.
Solved Examples
Example 1: Example 1: Tiling a Room
Problem: Ria’s room is 6 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 = 6 × 4 = 24 m²
Step 2: Convert tile side: 50 cm = 0.5 m
Step 3: Tile area = 0.5 × 0.5 = 0.25 m²
Step 4: Number of tiles = 24 ÷ 0.25 = 96
Answer: Ria needs 96 tiles.
Example 2: Example 2: Cost of Painting a Wall
Problem: A wall is 10 m long and 4 m high. Painting costs ₹30 per sq m. Find the total cost.
Solution:
Step 1: Wall area = 10 × 4 = 40 m²
Step 2: Cost = 40 × 30 = ₹1,200
Answer: The total painting cost is ₹1,200.
Example 3: Example 3: Cost of a Plot of Land
Problem: Arjun’s father buys a rectangular plot that is 25 m long and 18 m wide. The rate is ₹500 per sq m. What is the total cost?
Solution:
Step 1: Area = 25 × 18 = 450 m²
Step 2: Cost = 450 × 500 = ₹2,25,000
Answer: The total cost is ₹2,25,000.
Example 4: Example 4: Comparing Two Rooms
Problem: Room A is 8 m × 5 m. Room B is 7 m × 6 m. Which room has a greater area and by how much?
Solution:
Step 1: Area of Room A = 8 × 5 = 40 m²
Step 2: Area of Room B = 7 × 6 = 42 m²
Step 3: Difference = 42 − 40 = 2 m²
Answer: Room B has a greater area by 2 m².
Example 5: Example 5: Finding a Missing Dimension
Problem: A rectangular garden has an area of 180 m². Its length is 15 m. Find the breadth.
Solution:
Step 1: Area = Length × Breadth
Step 2: 180 = 15 × Breadth
Step 3: Breadth = 180 ÷ 15 = 12 m
Answer: The breadth is 12 m.
Example 6: Example 6: Carpet for a Square Hall
Problem: A square hall has a side of 12 m. Carpet costs ₹150 per sq m. Find the total cost of carpeting the hall.
Solution:
Step 1: Area = 12 × 12 = 144 m²
Step 2: Cost = 144 × 150 = ₹21,600
Answer: The total cost is ₹21,600.
Example 7: Example 7: L-Shaped Room
Problem: An L-shaped room is made of two parts: 8 m × 5 m and 4 m × 3 m. How many square metres of flooring is needed?
Solution:
Step 1: Area of part 1 = 8 × 5 = 40 m²
Step 2: Area of part 2 = 4 × 3 = 12 m²
Step 3: Total area = 40 + 12 = 52 m²
Answer: 52 m² of flooring is needed.
Example 8: Example 8: Wall with a Door
Problem: A wall is 8 m long and 3 m high. It has a door of 2 m × 1 m. Find the area to be painted.
Solution:
Step 1: Wall area = 8 × 3 = 24 m²
Step 2: Door area = 2 × 1 = 2 m²
Step 3: Area to paint = 24 − 2 = 22 m²
Answer: The area to be painted is 22 m².
Example 9: Example 9: Flowerbeds in a Garden
Problem: Neha’s rectangular garden is 20 m × 15 m. She makes two square flowerbeds of side 3 m each. Find the remaining area.
Solution:
Step 1: Garden area = 20 × 15 = 300 m²
Step 2: One flowerbed = 3 × 3 = 9 m²
Step 3: Two flowerbeds = 2 × 9 = 18 m²
Step 4: Remaining area = 300 − 18 = 282 m²
Answer: The remaining area is 282 m².
Example 10: Example 10: Unit Conversion before Calculating
Problem: A rectangular cloth is 3 m long and 150 cm wide. Find its area in sq cm.
Solution:
Step 1: Convert length: 3 m = 300 cm
Step 2: Area = 300 × 150 = 45,000 cm²
Answer: The area is 45,000 cm².
Real-World Applications
Real-life uses of area word problems:
- Home renovation: Calculating tiles, paint, or wallpaper for rooms.
- Farming: Measuring field area for seeds, fertiliser, and irrigation planning.
- Shopping: Buying the right amount of fabric, carpet, or wrapping paper.
- Construction: Planning material for walls, floors, roofs, and plots.
- School projects: Cutting chart paper, covering books, making posters.
Key Points to Remember
- Read the problem carefully and identify the shape (rectangle, square, composite).
- Extract the dimensions and check that units match before calculating.
- Use the correct formula: rectangle = l × b, square = s × s.
- For tiling: number of tiles = total area ÷ area of one tile.
- For cost: total cost = area × rate per sq unit.
- For shapes with holes (doors, windows), subtract the hole’s area from the total.
- For composite shapes, split into rectangles, calculate each area, and add.
- Always write the answer with correct units (m², cm²).
Practice Problems
- A classroom is 9 m long and 7 m wide. Find its area.
- How many square tiles of side 25 cm are needed to tile a floor that is 5 m × 4 m?
- A rectangular park is 60 m × 40 m. A path of 2 m width runs along the inside boundary. Find the area of the path.
- Kavi’s garden is 30 m long. Its area is 450 m². Find the breadth.
- A wall 12 m × 4 m has two windows each 1.5 m × 1 m. Find the area to be whitewashed.
- Which has more area: a square room of side 8 m or a rectangular room of 10 m × 6 m?
- Aditi buys a plot of 20 m × 16 m at ₹800 per sq m. What is the total cost?
- An L-shaped hall is made of two rectangles: 12 m × 6 m and 8 m × 4 m. Find the total floor area.
Frequently Asked Questions
Q1. What are area word problems?
Area word problems are questions that describe a real-life situation (like tiling a room or painting a wall) and ask you to calculate the area or use the area to find cost, number of tiles, or a missing dimension.
Q2. How do you solve area word problems?
Read the problem, identify the shape, extract the dimensions, choose the correct formula (l × b for rectangles, s × s for squares), and calculate. Check that all measurements are in the same unit.
Q3. What if the units are different in a problem?
Convert all measurements to the same unit before calculating. For example, if length is in metres and breadth is in centimetres, convert metres to centimetres (or vice versa) first.
Q4. How do you find the number of tiles needed?
Divide the total floor area by the area of one tile. Make sure both areas are in the same unit. Number of tiles = floor area ÷ tile area.
Q5. How do you find the cost of painting a wall?
Calculate the wall area (length × height), then multiply by the cost per square metre. If the wall has doors or windows, subtract their area first.
Q6. How do you handle L-shaped or T-shaped rooms?
Split the shape into two or more rectangles. Find the area of each rectangle separately and add them together for the total area.
Q7. What is the difference between area and perimeter word problems?
Area problems ask how much surface a shape covers (measured in square units). Perimeter problems ask how much boundary or fencing is needed (measured in linear units like metres).
Q8. How do you find a missing side when area is given?
Use the formula in reverse. For a rectangle: missing side = area ÷ known side. For a square: side = √area.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Area word problems involving rectangles, squares, and composite shapes are part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
