Topics · Primary Maths · Area & Perimeter
Area and perimeter: what each one measures
Two numbers about the same shape, answering two different questions. Perimeter is how far it is round the edge. Area is how much surface is inside. Almost every lost mark on this topic is one being given when the other was asked for.
- 401 exam papers analysed
- appears in 96% of P6 Maths papers
- ~4 min read
01 Two different questions
Perimeter is a distance: walk all the way round the edge and count how far you went. It is measured in ordinary length units — cm, m, km.
Area is a covering: how many squares it takes to fill the inside. It is measured in square units — cm², m² — and the little 2 is not decoration, it is the whole difference.
Here is the same rectangle asked both ways. Nothing about the shape changed; only the question did.
02 Where the area formula comes from
Area is counting squares. Length × width is simply a quicker way of counting them: 3 rows of 5 squares is 5 × 3, and you never have to count one by one.
That is worth holding on to, because it explains what to do when a shape is not a rectangle. Cut it into rectangles, count each, add them up. A P6 composite-figure question is that idea and nothing more.
- Rectangle: length × width. The 5 by 3 above holds 15 squares.
- Square: side × side, because a square is a rectangle whose sides match.
- Triangle: ½ × base × height. A triangle is half of a rectangle drawn round it, so it holds half as many squares.
- Any other shape: cut it into rectangles you can do, work out each one, and add.
03 Same perimeter, different area
These two rectangles both measure 16 cm all the way round. One holds 15 squares and the other holds 7.
So the two numbers are genuinely independent: knowing one tells you nothing about the other. A question that gives you the perimeter and asks for the area has always given you something else as well — go and find it.
04 Reading the question
The words a paper uses are fairly reliable, and worth learning as signals.
- Fencing, edging, ribbon, skirting, walking round, how far → perimeter. Anything that follows the edge.
- Carpet, paint, turf, tiles, covering, how much surface → area. Anything that fills the inside.
- Check your units before you write the answer. An answer in cm when the question wanted cm² is the wrong quantity, not a slip of the pen — and vice versa.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- perimetersaypuh-RIM-uh-tuhmore than oneperimeters
The total distance round the outside of a shape. Add up the lengths of all its sides. Measured in cm, m and so on.
- areasayAIR-ee-uhmore than oneareas
The amount of surface inside a shape, counted in squares. Measured in square units — cm², m².
- square centimetre, written cm²sayskwair SEN-ti-mee-tuhmore than onesquare centimetres
A square measuring one centimetre each way. Area is how many of these fit inside a shape.
- basesaybayssmore than onebases
The side of a triangle you measure the height from. Any of the three sides can be the base — you choose, and the height must match your choice.
- heightsayhitemore than oneheights
The straight-up distance from the base to the far corner, meeting the base at a right angle. Not the length of a sloping side.
- composite figuresayKOM-puh-zit FIG-uhmore than onecomposite figures
A shape made of two or more simpler shapes joined together. Cut it back into rectangles to find its area.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P3
Perimeter by adding up the sides, and area by counting squares on a grid.
Practise P3 Area & Perimeter — 10 questions →38% of P3 papers
- P4
Area and perimeter of squares and rectangles by formula, and finding a missing side from a given area.
Practise P4 Area & Perimeter — 10 questions →66% of P4 papers
- P5
Triangles, and composite figures cut into rectangles.
Practise P5 Area & Perimeter — 10 questions →77% of P5 papers
- P6
Several shapes combined, shaded regions found by subtracting one area from another, and working backwards from an area to a length.
Practise P6 Area & Perimeter — 10 questions →96% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“I found the area, and the answer is 15 cm.”
Area is measured in square units, so it is 15 cm². The unit is part of the answer, and cm and cm² are answers to different questions.
“Both rectangles have a perimeter of 16 cm, so their areas match too.”
They do not. 5 by 3 holds 15 squares and 7 by 1 holds 7, both with 16 cm round the outside. Perimeter fixes nothing about area.
“For the triangle I multiplied the base by the sloping side.”
The height has to meet the base at a right angle. The sloping side is longer than the height, so this always gives an answer that is too big.
“The shape is L-shaped, so there is no formula for it.”
There does not need to be. Cut it into two rectangles, find each area, and add them. That is what composite-figure questions are testing.
“To find the perimeter of a rectangle I add the length and the width.”
That is only half of it. There are two lengths and two widths, so it is length + width + length + width — or double the sum of the two.
Now try it
40 questions across 4 levels, marked as you go with the working shown.