11 plus Perimeter, Area & Volume questions

What a Perimeter, Area & Volume question looks like

Perimeter, Area & Volume is the measuring topic in 11 plus maths. A question gives a shape with its measurements already on it and asks for a number back: how far it is all the way round, how much flat surface it covers, or how much space it holds inside. Its two nearest neighbours ask something different: 2D Shapes & Properties and 3D Shapes & Nets ask a child to name a shape and count its sides or faces, whereas this topic never asks what a shape is called, only how big it is.

The shapes are deliberately plain. Almost every question is built on a rectangle, a cuboid, or a straight-sided figure made by joining two rectangles into an L or a T. Regular polygons appear when a perimeter is shared between equal sides, and circles turn up only to hand over the length of a square’s side, never with pi. The difficulty sits in the units and in the last step: measurements arrive in millimetres, centimetres, metres and litres, the answer is often wanted in a unit the question never used, and many ask for a cost or a tile count rather than the measurement itself.

Example one: which of the three is it?

A rug is 7 m long and 3 m wide. What is the distance all the way round the edge of the rug?

Distance all the way round means walking the edge. A rectangle has two long sides and two short ones, so that is 7 + 3 + 7 + 3 = 20. The rug was measured in metres, so the answer is in metres.

The answer is 20 m.

The option that catches children is 21 m. That is 7 × 3, which tells you how much floor the rug covers, not how far it is round the edge. Covering is measured in square metres, so 21 could only ever have been 21 m².

Example two: a corner taken out

A playground is drawn as an L. The whole shape is 10 m across and 8 m from top to bottom, and a rectangle 4 m across and 5 m tall has been taken out of the bottom-right corner. What is the area of the playground?

The quicker method is to pretend the corner is still there. The full rectangle would be 10 × 8 = 80 m². The piece taken out is 4 × 5 = 20 m². Take one away from the other: 80 - 20 = 60 m².

The answer is 60 m².

80 m² is the tempting wrong answer: it is the whole rectangle with the corner still in place. 40 m² catches a child who finds the missing piece, 20 m², and then doubles it instead of taking it away.

Example three: the answer in different units

A rectangular banner measures 2.5 m by 1.2 m. What is its area in cm²?

Change the measurements into centimetres first. 2.5 m is 250 cm and 1.2 m is 120 cm. Now multiply: 250 × 120 = 30,000.

The answer is 30,000 cm².

300 cm² is the trap, and it is the commonest slip in the topic. It comes from working in metres, 2.5 × 1.2 = 3, then multiplying by 100 because 1 m is 100 cm. But a square measure converts twice over: a square metre is 100 cm by 100 cm, which is 10,000 cm². Three square metres is 30,000 cm², not 300.

How to answer it

1. Work out which of the three it wants. How far round is perimeter, how much surface is area, how much space inside is volume. The units on the options give it away: cm or m for round the edge, cm² for surface, cm³ for space inside.
2. Sort the units out before calculating. If one measurement is in metres and another in centimetres, put both into the smaller unit first, and convert at the start when the answer is wanted in a unit the question did not use. A square measure converts twice, a space measure three times.
3. Break an awkward shape into rectangles. An L or a T is either two rectangles added together or one big rectangle with a corner taken out. Pick whichever leaves numbers you can handle in your head.
4. Do the calculation, then write the unit on the answer. The right number with the wrong unit scores nothing, and a wrong unit usually means the wrong question got answered.
5. Read the question once more. Plenty of these want something after the measurement: the cost at £6 a metre, how many 3 m lengths of edging, how many tins of paint.

Common mistakes

• Answering the other question, or half of it. For a garden 8 m by 5 m the perimeter is 26 m and the area is 40 m², and both sit in the options. So does 13, from adding 8 and 5 once and forgetting the other two sides.
• Converting a square measure as though it were a length. A banner of 3 m² is 30,000 cm², not 300 cm². Square units use the length factor twice, so 1 m² is 10,000 cm² and 1 cm² is 100 mm².
• Forgetting the piece that was taken away. When a shed stands in a corner of a lawn, or a window sits in a wall, the whole rectangle is always one of the options. It is the number a child reaches first and it is never the answer.
• Losing the third measurement in a volume. A box 5 cm by 3 cm by 2 cm holds 30 cm³, but 15 cm³ (5 × 3) and 6 cm³ (3 × 2) both appear, each from multiplying two of the three and stopping.
• Stopping one step early. If a tin of paint covers 4 m² and the wall needs 13.5 m², then 13.5 ÷ 4 = 3.375, so the answer is 4 tins. Part of a tin still has to be bought, and 3 is sitting in the options.

How to practise 11 plus Perimeter, Area & Volume questions

This is a topic where a child can get every calculation right and still lose the mark, so mark the units separately from the numbers: they are two different things to fix. It is worth reaching early in an eleven plus programme, because the unit habits take a while to settle. A tape measure round the house does more for a feel for a metre than another page of sums, and short and regular beats long and occasional, as we set out in how much 11 plus practice a child needs each day. 11+ Daily has a Perimeter, Area & Volume project alongside the other maths topics, on laptop, tablet or phone, and the full list is on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

Questions parents ask