Introduction
In Primary 3 Maths, you learnt about area and perimeter. And in Primary 4, you will learn how to find unknown sides of rectangles and squares when the areas and perimeters are given. This can be confusing. But do not worry — this guide simplifies the concepts for you and the questions will become much easier.
What this guide covers:
1. Recall (P3): Perimeter of rectangles and squares
2. How to find missing sides when the perimeter is given
3. Recall (P3): Area of rectangles and squares
4. How to find missing sides when the area is given
5. Heuristic: Dividing a rectangle into squares
6. Common mistakes to avoid
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1. Recall (P3): Perimeter of rectangles and squares
Perimeter means the outline of a shape.
The outline of the square is formed by 4 equal lengths.
The outline of rectangle is formed 1 pair of equal lengths and 1 pair of equal breadths.
The outline of the triangle is formed by 3 straight lines.
Perimeter can also mean the distance around a shape. Imagine walking all the way around your school field — the distance you walk is the perimeter.
Measurement Units
Perimeter is a length measurement. Units: cm, m, km.
If a shape has a perimeter of 15 cm, then its outline is 15 cm long.
A running track with a 400−m perimeter means one lap is 400 m.
How to Calculate Perimeter of Rectangles and Squares?
Example 1 (Rectangle)
The diagram above shows a rectangular school field. The perimeter of the school field can be calculated using two methods:
Method 1 (add up all the sides):
110 m + 75 m + 110 m + 75 m = 370 m (ans)
Method 2 (add the length and breadth then multiply by 2):
110 m + 75 m = 185 m
2 × 185 m = 370 m (ans)
Example 2 (square)
The diagram above shows a square piece of paper. Each side of the paper measures 15 cm. The perimeter of the square paper can be calculated as follows:
15 cm + 15 cm + 15 cm + 15 cm = 60 cm (ans) OR
4 × 15 cm = 60 cm (ans)
2. How to find missing sides when the perimeter is given
Example 1 (Square with unknown side)
The square shown below has a perimeter of 24 cm. What is the length of each side of the square?
Length of each side of the square = 24 cm ÷ 4
= 6 cm (ans)
Example 2 (Rectangle with unknown side)
The diagram shown below represents a rectangular swimming pool. It has a perimeter of 150 m. What is the breadth of the swimming pool?
Method 1
Two lengths of the pool = 50 m + 50 m = 100 m
Two breadths of the pool = 150 m − 100 m = 50 m
Breadth of the pool = 50 m ÷ 2 = 25 m (ans)
Method 2
Length of pool + Breadth of pool = 150 m ÷ 2 = 75 m (small total of one group)
Breadth of pool = 75 m − 50 m (length) = 25 m (ans)
40 cm ÷ 2 = 20 cm (ans)
3. Recall (P3): Area of rectangles and squares
Area means the space covered inside a shape.
Example 1 (m2)
Imagine putting identical square tiles together.
There are 4 rows and 5 columns on the floor, which makes 4 × 5 = 20 tiles. We say that the area of the floor is 20 square units.
When each tile measures 1 metre by 1 metre exactly, then the area of each square is 1 m2 (read as 1 square metre, NOT 1 metre square).
Since there are 20 tiles in the rectangle, we say the area of the rectangular floor is 20 m2.
Example 2 (cm2)
Imagine dividing a rectangle into small identical squares.
The piece of paper above is divided into unit squares of the same size. There are 4 rows and 6 columns on the floor, which makes 4 × 6 = 24 squares.
Each square measures 1 cm by 1 cm. We say that the area of each square is 1 cm2 (read as 1 square centimetre, NOT 1 centimetre square).
Since there are 24 squares in the rectangle, we say the area of the rectangular piece of paper is 24 cm2.
Measurement Units
The measurement units for area are cm2 , m2 and km2 (at secondary level).
If a shape has an area of 15 cm2, it means there are 15 unit squares inside and each unit square measures 1 cm by 1 cm.
If a school field has an area of 7000 m2, it means there are 7000 unit squares inside, and each unit square measures 1 m by 1 m.
How to calculate area of rectangles and squares?
Example 1
A rectangle measures 8 cm by 5 cm. What is the area (in cm2) of the rectangle?
Solution:
Area of the rectangle = 8 cm × 5 cm = 40 cm2 (ans)
Note:
It is not possible to divide the shapes into small unit squares each time we calculate area because of time constraint. Also the shapes provided are not drawn to scale.
To quickly calculate area of rectangles or squares, we simply apply the formula
Area of rectangle (or square) = Length × Breadth
Example 2
The diagram above shows a rectangular school field. What is the area of the school field?
Area of school field = 110 m × 75 m = 8250 m2 (ans)
Example 3
The diagram above shows a square. Each side of the paper measures 15 cm. What is the area of the square?
Area of square = 15 cm × 15 cm = 225 cm2 (ans)
4. How to find missing sides when the area is given
Example 1 (rectangle)
The diagram shown below represents a rectangular swimming pool. It has an area of 1000 m2 and a length of 50 m. What is the breadth of the swimming pool?
Breadth of swimming pool = 1000 m2 ÷ 50 m = 20 m (ans)
Example 2 (rectangle)
The diagram shown below represents a rectangular piece of wood. It has an area of 500 cm2 and a breadth of 25 cm. What is the length of the piece of wood?
Length of piece of wood = 500 cm2 ÷ 25 cm = 20 cm (ans)
Example 3 (square)
The diagram above shows a square. It has an area of 36 cm2 What is the length of each side of the square?
36 cm2 = 6 cm × 6 cm
So the length of each side of the square is 6 cm. (ans)
Common mistake (confusion between area and perimeter):
36 cm2 ÷ 4 = 9 cm. (wrong answer)
The working above would divide the square into four equal parts. Each part has an area of 9 cm2. The numerical value of ‘9’ does not represent the length of the square.
Also we can check:
If the length of the square is 9 cm, then its area would be 9 cm × 9 cm = 81 cm2
But the question stated the area as 36 cm2.
We only carry out divide 36 ÷ 4 IF 36 represents the perimeter of the square.
5. Heuristic: Dividing a rectangle into squares
Example 1 (No leftover area)
A piece of paper measuring 8 cm by 6 cm is to be cut into identical 2–cm squares. What is the maximum number of 2−cm squares that can be cut out from the paper?
See that we can divide the paper into 2−cm squares as shown above.
Along the length, there are 8 cm ÷ 2 cm = 4 squares.
Along the breadth, there are 6 cm ÷ 2 cm = 3 squares.
The maximum number of 2−cm squares that can be cut = 4 × 3 = 12 (ans)
Alternative Method:
Total area = 8 cm × 6 cm = 48 cm2
Area of a small square = 2 cm × 2 cm = 4 cm2
Maximum number of 2−cm squares that can be cut out = 48 cm2 ÷ 4 cm2 = 12 (ans)
Caution! This alternative method only works if the length of the small square divides both length and breadth measurements exactly.
Example 2 (With leftover area)
A piece of paper measuring 8 cm by 6 cm is to be cut into identical 3–cm squares. What is the maximum number of 3−cm squares that can be cut out from the paper?
See that we can divide the paper into 3−cm squares as shown above.
Along the length, there are 8 cm ÷ 3 cm ≈ 2 squares (rounded down)
Along the breadth, there are 6 cm ÷ 3 cm = 2 squares.
The maximum number of 3−cm squares that can be cut = 2 × 2 = 4 (ans)
Common mistake: treating area like other measurements
The student thinks:
Area of rectangle = 8 × 6 = 48 cm2
Area of small square = 3 × 3 = 9 cm2
Divide: 48 ÷ 9 = 5 (round down)
So they conclude there are 5 squares, but this is incorrect as this assumes the rectangle can be filled perfectly with small squares just by dividing the areas.
Example 3 (Division by highest common factor)
A rectangular wooden board measures 48 cm by 36 cm. It is to be cut into identical squares. What is the largest possible length of each square so that no wood is wasted?
Solution:
We need to find a suitable length that divides both 48 and 36 without remainder.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Since the question requires the largest possible square, we select the highest common factor, which is 12.
The largest possible side of each square is 12 cm.
6. Common Mistakes to Avoid
When solving area and perimeter problems, many students fall into the same traps. With these reminders, you can avoid losing marks in common traps and solve area-and-perimeter questions more confidently.
Let’s look at the most common ones:
Mixing up formulas
Mistake: Students sometimes add length and breadth when they should multiply, or they multiply when they should add. For example, writing Area = length + breadth instead of Area = length × breadth.
Why it happens: Both formulas use the same measurements (length and breadth), so it is easy to confuse them.
How to avoid: Always ask yourself, “Am I finding the space inside (area) or the distance around (perimeter)?” A good memory trick:
Perimeter → outline
Area → space covered
Forgetting units
Mistake: Writing “96” instead of “96 cm2 ” when finding area, or writing “24” instead of “24 cm” for perimeter.
Why it happens: Students focus on the numbers and forget to attach the units. In exams, this can cost marks.
How to avoid: Train yourself to always write the unit after the number.
Remember:
Perimeter is measured in length units (cm, m, km).
Area is measured in square units (cm2, m2, km2).
Counting leftover pieces when cutting squares
Mistake: Students divide total area by the area of one square, without checking if the sides fit evenly. For example, 48 ÷ 9 = 5 remainder, so they wrongly say 5 squares fit.
Why it happens: They forget that partial squares cannot be used.
How to avoid: Always divide the length by the side of the square, and the breadth by the side of the square. Multiply the results. This ensures only full squares are counted.
Example: An 8 cm by 6 cm rectangle cut into 3 cm squares → (8 ÷ 3 = 2 r2) and (6 ÷ 3 = 2 exactly). So only 2 × 2 = 4 squares fit. The leftover strip cannot be used.
Thinking perimeter is always larger than area
Mistake: Some students believe the perimeter must always be greater than the area. This is not true.
Example: A square of side 2 cm → perimeter = 8 cm, area = 4 cm2 (perimeter is bigger). But a square of side 20 cm → perimeter = 80 cm, area = 400 cm2 (area is bigger).
How to avoid: Remember that area and perimeter measure different things. They cannot be directly compared as “bigger” or “smaller”.
Not drawing diagrams
Mistake: Jumping into calculation without sketching the rectangle or square.
Why it happens: Students want to save time, but they end up making careless errors.
How to avoid: Even a quick rectangle with numbers labelled helps you see clearly whether to add, multiply, or divide.
Need More Revision Notes for Primary School Math?
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