Primary 4 Maths: Area & Perimeter
Area and perimeter of rectangles and squares, composite rectilinear figures, and finding an unknown side — worked examples for the P4 Maths syllabus.
Most schools typically cover this topic in Term 3, around weeks 3–5 — though every school sets its own sequence.
Primary 4 is where area and perimeter stop being one blurred idea and become two separate skills. Area is the flat space a shape covers, measured in square units (cm², m²): for a rectangle it's length × breadth, and for a square, side × side. Perimeter is the distance around the outside, measured in plain units (cm, m): 2 × (length + breadth) for a rectangle, or 4 × side for a square. Under the 2021 MOE Mathematics syllabus, P4 extends both formulas to composite rectilinear figures — shapes built by joining rectangles and squares together, like an L or a step — and to problems where one side is missing and has to be worked out first.
Composite figures are the real test of the topic. A single rectangle rarely trips a child up; a figure with only some sides labelled does, because area needs both missing dimensions found first, while perimeter needs every outer edge counted once, labelled or not. The habit worth building now is simple: before calculating anything, mark in every side length — the given ones and the ones that have to be worked out — directly on the figure.
P4 Area & Perimeter: the mistakes to watch for
- Mixing up area and perimeter. Multiplying when the question asks for the distance around, or adding when it asks for the space covered. The units are the giveaway: cm² can only come from a multiplication (area); a plain cm answer for a whole shape's boundary is a sum of sides (perimeter).
- Skipping an unlabelled side in a composite figure's perimeter. Every outer edge counts once, including the ones the diagram doesn't print a number next to — those have to be calculated first, not ignored.
- Guessing an unknown side instead of matching opposite edges. In a rectilinear figure, the horizontal pieces on top must add up to the bottom length, and the vertical pieces on one side must add up to the opposite side's length. That's subtraction, not a guess.
- Multiplying before both sides of a rectangle piece are known. A composite figure's area is usually the sum (or difference) of two or more rectangles — each piece needs its own length and breadth pinned down before any multiplying starts.
P4 Area & Perimeter: shapes and formulas
P4 Area & Perimeter: easy warm-ups
Easy: area of a rectangle
A rectangle is 12 cm long and 5 cm wide. Find its area.
Show the worked solution
Area = length × breadth = 12 × 5 = 60 cm².
Easy: perimeter of a square
A square tile has sides of 9 cm. Find its perimeter.
Show the worked solution
Perimeter = 4 × side = 4 × 9 = 36 cm.
Easy: perimeter of a rectangle
A rectangle has a length of 15 cm and a breadth of 8 cm. Find its perimeter.
Show the worked solution
Perimeter = 2 × (length + breadth) = 2 × (15 + 8) = 2 × 23 = 46 cm.
Easy: area of a square
A square garden plot has sides of 11 m. Find its area.
Show the worked solution
Area = side × side = 11 × 11 = 121 m².
P4 Area & Perimeter: exam-style questions
Exam: finding a missing length from area
A rectangle has an area of 84 cm² and a breadth of 7 cm. Find its length.
Show the worked solution
Length = area ÷ breadth = 84 ÷ 7 = 12 cm.
Check: 12 × 7 = 84. ✓
Exam: finding a missing breadth from perimeter
A rectangle has a perimeter of 50 cm. Its length is 17 cm. Find its breadth.
Show the worked solution
Half the perimeter = length + breadth, so length + breadth = 50 ÷ 2 = 25 cm.
Breadth = 25 − 17 = 8 cm.
Exam: square, from perimeter to area
A square has a perimeter of 52 cm. Find its area.
Show the worked solution
Side = perimeter ÷ 4 = 52 ÷ 4 = 13 cm.
Area = 13 × 13 = 169 cm².
Exam: area of an L-shaped composite figure
The figure above is made from a 20 cm by 14 cm rectangle with a rectangular corner of 8 cm by 6 cm cut away. Find the area that remains.
Show the worked solution
Area of the full rectangle = 20 × 14 = 280 cm².
Area removed = 8 × 6 = 48 cm².
Remaining area = 280 − 48 = 232 cm².
Exam: finding two unmarked sides of a composite figure
An L-shaped figure has a bottom edge of 20 cm and a left edge of 14 cm. A rectangular notch has been cut from the top-right corner: its lower edge measures 8 cm and its right-hand edge measures 8 cm. Find (a) the length of the top edge and (b) the height of the notch's inner vertical edge.
Show the worked solution
(a) The top edge and the notch's 8 cm lower edge together must equal the bottom: top = 20 − 8 = 12 cm.
(b) The notch's inner vertical edge and the 8 cm right-hand edge together must equal the left edge: notch height = 14 − 8 = 6 cm.
P4 Area & Perimeter: PSLE-challenge preview
PSLE challenge: a T-shaped stage
A stage is made from a rectangle 20 m by 12 m, with a smaller platform 6 m by 4 m attached to the middle of one of the 20 m sides, sticking outward. Find (a) the total area of the stage and (b) its perimeter.
Show the worked solution
(a) Rectangle area = 20 × 12 = 240 m². Platform area = 6 × 4 = 24 m².
Total area = 240 + 24 = 264 m².
(b) The 6 m base of the platform is no longer on the boundary — it's replaced by the platform's other three sides: two 4 m sides and one 6 m far side.
Original rectangle perimeter = 2 × (20 + 12) = 64 m. Remove the 6 m base, add 4 + 6 + 4 = 14 m.
Perimeter = 64 − 6 + 14 = 72 m.
PSLE challenge: a rectangle from a length ratio
A rectangular garden's length is 3 times its breadth. Its perimeter is 96 m. Find its area.
Show the worked solution
Perimeter = 2 × (length + breadth), so length + breadth = 96 ÷ 2 = 48 m.
Length + breadth = 3 units + 1 unit = 4 units = 48 m, so 1 unit = 12 m.
Breadth = 12 m, length = 3 × 12 = 36 m.
Area = 36 × 12 = 432 m².
Check: perimeter = 2 × (36 + 12) = 96 m. ✓
PSLE challenge: a picture frame border
A rectangular photo frame has outer measurements of 30 cm by 24 cm. The photo it holds measures 24 cm by 18 cm. Find the area of the wooden border around the photo.
Show the worked solution
Area of the outer rectangle = 30 × 24 = 720 cm².
Area of the photo = 24 × 18 = 432 cm².
Area of the border = 720 − 432 = 288 cm².
Check: the border is 30 − 24 = 6 cm narrower in total width and 24 − 18 = 6 cm narrower in total height, so it's an even 3 cm wide all the way round. ✓
P4 Area & Perimeter: how to practise this topic
Composite figures reward one habit above all others: writing every side length onto the diagram — given and worked-out alike — before any formula gets used. A child who can reliably find a missing side from matching edges has laid the groundwork for the shaded-region questions in P6 Circles, which mix curved and straight pieces the same way P4's rectilinear figures mix rectangles.
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 4 Area & Perimeter includes the concepts below. (P4-M-07 is Test Paper's own topic code, not an MOE reference.)
- Area of rectangle
- Area of square
- Perimeter of rectangle
- Perimeter of square
- Area of composite figures
- Perimeter of composite figures
- Area and perimeter word problems
Before this topic
These topics feed into Area & Perimeter — if this one wobbles, check them first: Primary 4 Multiplication & Division.
Where to go next
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