Compound-shape questions — finding the area of an L-shape or a room with a missing corner — are an 11+ staple, and they are one of the biggest mark-losers in the whole maths paper. The trick is always the same: split the shape into rectangles, then label every single edge, including the two the question deliberately left off the diagram. This page teaches area and perimeter properly, with a fully worked compound-shape example, the exam traps that catch children out, and links to the free graded worksheets and timed mocks that turn the method into a reflex.
What 11+ area and perimeter questions actually test
At 11+ level, area and perimeter means far more than the length-times-width rectangle. Examiners want to see whether a child can keep track of units, read a diagram carefully, and handle a shape that is not a neat rectangle. The core skills are: perimeter (the distance all the way round), area of rectangles and squares, area of right-angled triangles, and — the big one — compound shapes made of two or more rectangles joined together. Our free worksheet library grades every one of these across four tiers, Foundation, Developing, Secure and Greater Depth, so a child enters at the right level and climbs.
Here is the quick-reference box every pupil should know cold before an exam:
| Measure | Formula | Units |
|---|---|---|
| Perimeter of any shape | Add up every side | cm, m (length) |
| Area of a rectangle | length × width | cm², m² (squared) |
| Area of a square | side × side | cm², m² |
| Area of a triangle | (base × height) ÷ 2 | cm², m² |
| Area of a compound shape | Split into rectangles, add the areas | cm², m² |
Notice the golden rule hiding in that table: perimeter is a length, so it uses plain units; area is a covering, so it always uses squared units. Getting cm and cm² muddled is the single most common careless error, and in a GL multiple-choice paper the wrong unit is nearly always sitting there as a tempting answer option.
A fully worked compound-shape example
Picture an L-shaped garden. The diagram gives you an overall width of 10 m across the top, a full height of 8 m down the left side, a 6 m notch cut into the bottom-right corner that is 3 m deep. Two edges are left unlabelled on purpose. Here is the method, step by step.
- Split into rectangles. Draw one line to cut the L into a big rectangle on the left and a smaller rectangle on top, or a tall rectangle plus a wide one. Either split works — pick the cleaner one.
- Find the missing edges first. If the top is 10 m and the removed notch is 6 m wide, the remaining stub is 10 − 6 = 4 m. If the left side is 8 m and the notch is 3 m deep, the shorter height is 8 − 3 = 5 m. Never start multiplying until every edge is written on the diagram.
- Work out each rectangle's area. Rectangle A (the full left block): 4 m × 8 m = 32 m². Rectangle B (the wide lower block): 6 m × 5 m = 30 m².
- Add them. Total area = 32 + 30 = 62 m².
- Perimeter, separately. Walk right round the outside adding every edge: 10 + 8 + 4 + 5 + 6 + 3 = 36 m. Do not add the internal splitting line — it is not part of the outside.
An equally valid shortcut for area is subtraction: work out the whole 10 × 8 = 80 m² rectangle, then subtract the missing 6 × 3 = 18 m² corner, giving 80 − 18 = 62 m². Teach your child both, because the exam sometimes makes one route far quicker than the other.
Common mistakes and 11+ exam traps
- Mixing up area and perimeter. The question wording switches at the last second — "how much fencing?" means perimeter, "how much turf?" means area. Underline the actual question.
- Forgetting the squared unit. Writing 62 m instead of 62 m² on an area answer is a guaranteed lost mark, and the plain-unit distractor is always offered in the A–E options.
- Not finding the missing edges. Children multiply the numbers printed on the diagram and ignore the unlabelled sides. Label every edge before touching the calculator-free arithmetic.
- Adding the internal cut line to the perimeter. Only outside edges count towards perimeter.
- Halving errors on triangles. Base × height gives a rectangle; the triangle is half of it. The ÷ 2 is not optional.
How it appears in a real GL 11+ paper
In a typical GL Assessment maths paper — roughly 50 questions in 50 minutes, about a minute a question, multiple-choice with answers A–E marked on a separate OMR sheet, no calculator — area and perimeter usually shows up two or three times. One question is a straight rectangle, and at least one is a compound shape or a "find the missing length" reasoning question. Because the answers are pre-printed, a child who forgets the squared unit or adds the internal line will find their wrong answer waiting as a distractor, so accuracy matters as much as method. Practise under the clock with our free timed mock papers and the free papers hub, which drop this topic inside full exams. Regional note: GL dominates most areas now that CEM's separate tests were phased out around 2022–2023, while CSSE (Essex) and some independent papers ask longer free-response area questions, so children sitting those should practise showing full working, not just picking a letter.
Difficulty progression: Year 5 versus Year 6
A Year 5 / Foundation version reads: "A rectangle is 7 cm long and 4 cm wide. Find its area and perimeter." Area = 7 × 4 = 28 cm²; perimeter = 7 + 4 + 7 + 4 = 22 cm. One shape, both numbers given, no hidden edges.
A Year 6 / Greater Depth version reads: "An L-shaped room has an area of 62 m². The full width is 10 m and the full height is 8 m. A rectangular alcove has been removed. If the alcove is 3 m deep, how wide is it?" Now the child must reverse the method: whole rectangle 80 m², minus the room 62 m², leaves a 18 m² alcove; 18 ÷ 3 = 6 m wide. Same skill, worked backwards — exactly the reasoning jump the 11+ rewards.
How to use the free worksheets
- Diagnose: one Secure-tier sheet, unaided. Scoring under 70%? Drop a tier. Over 90%? Climb one.
- Little and often: 15–20 minutes daily beats a weekend marathon — retention lives in the gaps between sessions.
- Review errors out loud: the child explains what went wrong before you say a word. Self-diagnosis sticks.
- Fold into mocks: once a topic hits Greater Depth, let full timed mock papers keep it warm rather than more isolated drilling.
- Widen the net: pair area and perimeter with related geometry using our revision hub and the wider exam guides.
Every area and perimeter worksheet — with full Answer Keys and OMR sheets — is free in the worksheet library under the Maths tab. No card, no email wall.
Frequently asked questions
Is a calculator allowed for these questions?
No. GL 11+ maths papers are non-calculator, so children must be quick and accurate with mental and written methods like column multiplication and simple division.
What units should the answer use?
Perimeter uses plain length units (cm, m). Area always uses squared units (cm², m²). Volume, if asked, uses cubed units (cm³). Marking the right unit is part of the mark.
How much time should a child spend per question?
Aim for about a minute. A compound-shape question may take a little longer, so the strategy is to bank time on the quick rectangle questions and spend it where the reasoning is harder.