Spy maths quest: area

Quick answer

You can find the area of a shape by counting how many square units fit inside it, or by multiplying its length and width.

Learning outcome

By the end of this page, you will be able to find the area of rectangles and squares by counting squares or multiplying length and width.

• You can count squares to find the area of a shape
• You can use multiplication to find the area of rectangles
• You can measure the area of real things like your bedroom or garden
• You can solve a secret spy mission using area

Why this matters

Knowing how to find area helps you in many ways! When you're a spy, you need to know how big your secret base is. When you're planning a garden, you need to know how much space you have. When you're sharing a pizza, you need to know how big each slice is. Area is used in all sorts of jobs like building houses, designing clothes, and even playing video games!

How it works

Area is the amount of space inside a shape. To find the area of a rectangle or square:

1. Count how many squares fit inside the shape
2. Or multiply the length by the width

When we use squares to measure area, we call them square units. These could be square centimetres (cm²), square metres (m²), or square inches (in²).

Examples you can see

Let's imagine you're a secret agent and you need to find the area of different secret rooms.

Example 1: A small secret room

This room is 4 squares wide and 3 squares long. To find the area:

• Count all the squares: 4 × 3 = 12 squares
• Or multiply: 4 × 3 = 12 square units

So the area is 12 square units.

Example 2: A big garden

Your spy garden is 6 metres wide and 5 metres long. To find the area:

• 6 × 5 = 30 square metres

So the garden is 30 m².

Example 3: A square secret map

Your map is 4 squares on each side. To find the area:

• 4 × 4 = 16 square units

So the map is 16 square units.

Try it as a mini adventure

Imagine you're a secret spy agent on a mission to find a hidden treasure. You need to decode a message that says:

"The treasure is hidden in a room that is 6 squares long and 4 squares wide. Find the area to open the secret door."

Step 1: Draw a rectangle that is 6 squares long and 4 squares wide.

Step 2: Count all the squares inside the rectangle.

Step 3: Multiply the length and width to check your answer.

Step 4: The area tells you how many squares fit inside the room.

How many squares are in the room? 6 × 4 = 24 squares

Now you know the area is 24 square units. You can open the secret door and find the treasure!

Common mistakes

• Mistake: Thinking that area means the distance around the shape (that's perimeter).
• Why it happens: Confusing area with perimeter, which is the distance around the outside.
• Fix: Remember: area = inside space, perimeter = outside edge.

• Mistake: Forgetting to write the unit squared (²).
• Why it happens: Not remembering that area is measured in square units.
• Fix: Always write the unit with a small 2, like cm² or m².

• Mistake: Counting only the squares on the edge, not all the squares inside.
• Why it happens: Looking at the outside instead of the inside of the shape.
• Fix: Count every square inside the shape, including those in the middle.

Parent and carer guide

Help your child understand area by:

1. Using everyday objects to show area, like a book or a table
2. Playing with grid paper to draw shapes and count squares
3. Measuring real rooms or gardens to find area
4. Practising multiplication facts for area calculations
5. Encouraging them to explain their thinking, not just give answers

At home, you can ask questions like:

• "How much space does your bed take up?"
• "If you had a 3 by 4 square, how many tiles would fit inside?"
• "What's the area of your lunch box?"

Remember: it's okay to make mistakes. They help us learn!

Practice questions

1. What is the area of a rectangle that is 5 squares wide and 3 squares long?
2. A garden is 8 metres wide and 6 metres long. What is its area?
3. A square tile is 2 units on each side. What is its area?
4. What is the area of a shape that is 10 squares long and 2 squares wide?
5. A secret base is 7 squares wide and 5 squares long. What is its area?

Answers:

1. 5 × 3 = 15 square units
2. 8 × 6 = 48 square metres
3. 2 × 2 = 4 square units
4. 10 × 2 = 20 square units
5. 7 × 5 = 35 square units

FAQ

What is area?

Area is the amount of space inside a shape. You can think of it as how many squares fit inside a shape.

How do I find the area of a rectangle?

Multiply the length by the width. For example, a rectangle that is 4 units long and 3 units wide has an area of 4 × 3 = 12 square units.

Can I find area by counting squares?

Yes! If you have a grid, you can count how many squares fit inside a shape. This is helpful for small shapes or when learning.

Why do we write units squared?

We write units squared (like cm²) because area is measured in square units. One square unit is a square that is 1 unit long and 1 unit wide.

What if the shape is not a rectangle?

For other shapes, we can still find area by counting squares or using special formulas. But rectangles and squares are the easiest to start with!