Train maths quest: area
A story-led junior maths adventure using timetables, distances and platform clues to cover floors, gardens and maps with squares.
Quick answer
Area is the amount of space inside a shape, measured in square units. You can find the area of a rectangle by multiplying its length by its width.
Learning outcome
By the end of this page, you will be able to find the area of rectangles by counting squares or multiplying length and width.
- You can tell the difference between area and perimeter
- You can find the area of a rectangle using a grid or by multiplying
- You can solve a real-life problem using area
- You can explain how to find the area of a shape
Why this matters
Knowing how to find the area helps you solve problems in real life. When you're planning a garden, painting a wall, or laying tiles, you need to know how much space you have. In a train adventure, you might need to know how big a platform is to fit all the passengers or how much space a new train carriage needs.
How it works
Area is the amount of space inside a shape. For rectangles, we can find area by:
- Counting squares inside the shape
- Multiplying length by width
For example, if a rectangle is 4 squares long and 3 squares wide, we can count 12 squares or multiply 4 × 3 = 12.
Examples you can see
Let's imagine you're on a train journey and need to find the area of different parts of the train.
Example 1: The Train Carriage
Your train carriage is 6 metres long and 3 metres wide. To find the area:
- Method 1: Draw a grid and count squares
- Method 2: Multiply length by width
6 × 3 = 18 square metres
Example 2: The Platform
The platform at the station is 10 metres long and 4 metres wide.
Area = 10 × 4 = 40 square metres
Example 3: The Train Window
The window is 2 metres wide and 1 metre high.
Area = 2 × 1 = 2 square metres
Try it as a mini adventure
You are on a train journey from London to Edinburgh. Your task is to find the area of different parts of the train and station to help plan a new train carriage.
Step 1: You find a map of the train carriage. It is 5 squares long and 3 squares wide. What is the area?
Answer: 5 × 3 = 15 square units
Step 2: You are looking at the station platform. It is 12 squares long and 5 squares wide. What is the area?
Answer: 12 × 5 = 60 square units
Step 3: You want to design a new window for the train. It is 3 squares wide and 2 squares high. What is the area?
Answer: 3 × 2 = 6 square units
Step 4: You want to know how much space the entire train has. The train is 15 squares long and 4 squares wide. What is the area?
Answer: 15 × 4 = 60 square units
Common mistakes
- Mistake: Forgetting to write the unit (square metres, square centimetres)
- Why it happens: Children focus on the numbers and forget the label
- Fix: Always say "square units" or "square metres" after the answer
- Mistake: Confusing area with perimeter
- Why it happens: Both are about shapes, but area is about space inside and perimeter is about the outside edge
- Fix: Remember: Area = length × width; Perimeter = add all sides
- Mistake: Counting the squares on the edge instead of inside the shape
- Why it happens: It's easy to get confused when counting
- Fix: Use a ruler or grid to help count carefully
Parent and carer guide
Help your child understand area by:
- Using everyday objects like books, tables, or rooms to find area
- Playing with grid paper or drawing shapes to count squares
- Practising multiplication facts to help with area calculations
- Encouraging them to explain their thinking
- Noting if they are mixing up area and perimeter
Ask questions like:
- How much space does this table cover?
- Can you find the area of your bedroom?
- What's the difference between area and perimeter?
Remember: Area is about space inside a shape. It's like covering a shape with square tiles.
Practice questions
- What is the area of a rectangle that is 4 squares long and 3 squares wide?
- A garden is 8 metres long and 5 metres wide. What is its area?
- A book is 20 cm long and 15 cm wide. What is its area?
- A window is 100 cm wide and 75 cm high. What is its area?
- What is the area of a square with sides of 6 metres?
Answers:
- 4 × 3 = 12 square units
- 8 × 5 = 40 square metres
- 20 × 15 = 300 square centimetres
- 100 × 75 = 7,500 square centimetres
- 6 × 6 = 36 square metres
FAQ
What is area?
Area is the amount of space inside a shape. It's measured in square units like square metres or square centimetres.
How do you find the area of a rectangle?
You multiply the length by the width. For example, a rectangle that is 5 metres long and 3 metres wide has an area of 5 × 3 = 15 square metres.
Can you find area with counting?
Yes! You can draw a grid and count the squares inside the shape. This helps you understand what area means.
What's the difference between area and perimeter?
Area is the space inside a shape. Perimeter is the distance around the outside of a shape.
Why is area important?
Area helps us plan spaces like gardens, rooms, and playgrounds. It helps us know how much material we need for painting or tiling.