Year 5 Maths: Area of a Square

Understanding the Area of a Square

What is a Square?

A square is a special shape in geometry. It has four sides that are all the same length and four corners that are right angles (90 degrees).

What is Area?

The area of a shape tells us how much space is inside that shape. For a square, we can find out how much space is inside by using a simple formula.

The Formula for Area

To find the area of a square, we use this formula:

$$\text{Area} = \text{side} \times \text{side}$$

or we can also write it as:

$$\text{Area} = \text{side}^2$$

This means that you multiply the length of one side of the square by itself.

Example

Let’s say each side of the square is 4 cm long. To find the area, we do the following:

1. Identify the length of one side: 4 cm.
2. Use the formula: $$\text{Area} = 4 , \text{cm} \times 4 , \text{cm} = 16 , \text{cm}^2$$

So, the area of the square is 16 square centimetres (16 cm²).

Key Rules

1. All sides of a square are equal.
2. To find the area, always multiply the length of one side by itself.
3. The unit of area is always squared (like cm², m², etc.).

Tips and Tricks

• If you know the area and want to find the side length, you can do the opposite! Use the square root. For example, if the area is 25 cm², the side length is: $$\text{side} = \sqrt{25} = 5 , \text{cm}$$
• Draw a picture! Sometimes drawing the square and labelling the sides helps you visualise the problem better.
• Practice with real-life situations, like calculating the area of a square garden or a square table.

Questions to Test Your Understanding

Easy Level Questions

1. What is the area of a square with sides of 3 cm?
2. If one side of a square is 5 m, what is its area?
3. A square has sides of 2 cm. What is its area?
4. Calculate the area of a square with sides measuring 6 cm.
5. If a square has an area of 36 cm², what is the length of one side?
6. What is the area of a square with sides 1 m long?
7. A square has sides of 8 cm. What is the area?
8. If one side of a square is 10 cm, what is the area?
9. What is the area of a square if each side is 4 cm?
10. A square has an area of 49 cm². What is the length of one side?

Medium Level Questions

11. Find the area of a square with a side length of 12 cm.
12. If the area of a square is 64 m², what is the length of one side?
13. Calculate the area of a square with sides measuring 15 cm.
14. A square has a side length of 7 cm. What is its area?
15. What is the area of a square if each side is 9 m?
16. If one side of a square is 14 cm long, what is its area?
17. Find the area of a square with a side length of 11 cm.
18. A square has sides measuring 20 cm. What is the area?
19. If the area of a square is 81 cm², what is the length of one side?
20. Calculate the area of a square with sides measuring 13 cm.

Hard Level Questions

21. A square has an area of 100 m². What is the length of its sides?
22. If a square has a side length of 17 cm, what is its area?
23. Find the area of a square if each side is 18 m long.
24. A square has an area of 256 cm². What is the length of one side?
25. If one side of a square is 25 cm, what is the area?
26. Calculate the area of a square with a side length of 30 cm.
27. What is the area of a square with sides measuring 22 cm?
28. If the area of a square is 144 cm², what is the length of one side?
29. A square has an area of 196 m². What is the length of one side?
30. If one side of a square is 19 cm, what is its area?

Answers and Explanations

Easy Level Answers

1. 9 cm²
2. 25 m²
3. 4 cm²
4. 36 cm²
5. 6 cm
6. 1 m²
7. 64 cm²
8. 100 cm²
9. 16 cm²
10. 7 cm

Medium Level Answers

11. 144 cm²
12. 8 m
13. 225 cm²
14. 49 cm²
15. 81 m²
16. 196 cm²
17. 121 cm²
18. 400 cm²
19. 9 cm
20. 169 cm²

Hard Level Answers

21. 10 m
22. 289 cm²
23. 324 m²
24. 16 cm
25. 625 cm²
26. 900 cm²
27. 484 cm²
28. 12 cm
29. 14 m
30. 361 cm²

Now you have a better understanding of the area of a square! Keep practising, and soon it will be easy for you!