Compound shapes - the L-shaped and step-shaped figures made from two or more rectangles joined together - quietly lose more 11+ marks than almost any other geometry topic. The maths itself is only ever multiplication and addition, yet children drop the mark because they misread a missing side, muddle up area and perimeter, or rush a single subtraction. This guide gives you the two reliable methods (split-and-add for area, and a walk-around routine for perimeter), worked step by step, plus the exam traps that catch capable pupils under time pressure. Pair it with our free worksheets and a timed mini-mock and this becomes an easy source of marks rather than a leak.
What a compound shape actually is
A compound (or "composite") shape is any 2D shape built from simpler shapes stuck together - almost always rectangles at 11+ level. On a GL Assessment paper it appears as an L-shape, a T-shape or a rectangle with a smaller rectangle cut out of a corner. Some side lengths are given; at least one or two are deliberately left off, and finding those missing lengths is the real test. Everything else is arithmetic you already know from our area and perimeter worksheets.
Parent explainer: the examiner is not testing whether your child can multiply. They are testing whether the child can look at a picture, work out the hidden numbers, and stay organised. That is a habit you can coach at the kitchen table.
Finding the missing sides first
Before any calculation, fill in every side. On an L-shape the two "short" horizontal pieces must add up to the single long horizontal side, and the same is true vertically. So if the full width is 10 cm and one part is 6 cm, the missing part is 10 - 6 = 4 cm. Write the missing numbers straight onto the diagram. Children who skip this step are the ones who guess - and guessing is where marks vanish.
Area: the split-and-add method
Split the compound shape into two rectangles with one straight line, find each area, then add. Here is a worked L-shape.
- The shape is 10 cm wide and 8 cm tall overall, with a 4 cm by 5 cm rectangle removed from the top-right corner.
- Draw a line to split it into Rectangle A (the left column, 6 cm wide and 8 cm tall) and Rectangle B (the bottom-right piece, 4 cm wide and 3 cm tall).
- Area of A = 6 x 8 = 48 cm².
- Area of B = 4 x 3 = 12 cm².
- Total area = 48 + 12 = 60 cm².
Always write the little "squared" unit - a stray missing unit can be the difference between the intended answer and a distractor on the A-E multiple-choice sheet.
The subtract method (often faster)
The same shape can be solved by imagining the whole 10 x 8 rectangle and subtracting the cut-out corner: 10 x 8 = 80, then remove the missing 4 x 5 = 20, giving 80 - 20 = 60 cm². Same answer. Teach your child both, because for some shapes splitting is quicker and for others subtracting is - and matching answers by two methods is a brilliant self-check when time allows.
Perimeter: walk all the way around
Perimeter is the total distance around the outside. The classic error is to add only the numbers printed on the diagram and forget the sides that were left blank. Use the "walking finger" routine: start at one corner and travel around the whole outline, saying each length out loud, and do not stop until you are back where you started.
For the L-shape above, walking around gives: 10 + 5 + 6 + 3 + 4 + 8 = 36 cm. Notice that every side - including the two you calculated - is counted exactly once. A handy check: on any L-shape the sum of the horizontal sides equals twice the full width, and the vertical sides sum to twice the full height. Here that is (10 + 6 + 4) = 20 = 2 x 10, and (8 + 5 + 3) = 16 = 2 x 8. If your totals do not match, you have missed a side.
Quick reference: the formulas you need
| Measure | Rule | Unit |
|---|---|---|
| Area of a rectangle | length x width | cm² (squared) |
| Area of a compound shape | split into rectangles, add the areas | cm² |
| Perimeter | add every outside side, each once | cm |
| Missing side | total side - known part | cm |
Keep this alongside our fuller 11+ maths formula sheet so area, perimeter and volume all sit in one place at revision time.
Exam traps that cost marks
- Mixing up area and perimeter. Reread the final line of the question - "how much fencing?" means perimeter, "how much turf?" means area.
- Forgetting a missing side when adding the perimeter. Fill in every length on the diagram first.
- Wrong subtraction when finding a hidden length (6 from 10, not 10 from 6).
- Dropping units - cm² for area, cm for perimeter. Distractor answers on the A-E sheet often use the right number with the wrong unit.
- Overlapping rectangles. When you split, the two pieces must not share any area, or you will count a strip twice.
How it appears in the exam
In a GL paper you have roughly 50 questions in 50 minutes - about a minute each - answered in multiple-choice A-E format on a separate answer sheet, with no calculator. Compound-shape questions usually sit in the middle of the paper. A Year 4 or 5 pupil should master splitting simple L-shapes; a Year 6 pupil should handle cut-out corners and switch confidently between the split and subtract methods. Because scores are converted to a Standard Age Score (100 is average, and many grammar schools look for around 111 or above), turning these "should-get" geometry marks into "always-get" marks lifts the final SAS noticeably. Build the habit with our timed mocks and the wider 11+ maths guide, and slot compound shapes into your revision plan next to angles and worded-problem method.
Frequently asked questions
Is a calculator allowed for these questions?
No. GL 11+ papers are non-calculator, so the numbers are chosen to be manageable by hand. Practising quick multiplication tables and confident column subtraction makes compound-shape questions far faster.
Should my child split the shape or subtract from a big rectangle?
Either is correct - the answer is identical. Splitting is safest when the shape is a simple L; subtracting is quicker when a neat rectangle has one corner cut out. Learning both gives a built-in way to check the answer.
How long should one compound-shape question take?
Aim for about a minute, matching the paper's overall pace. If it is taking longer, the child is usually missing a side length - go back and label every side on the diagram before calculating.