Shape vocabulary is free marks: parallelogram, rhombus, vertices, faces, edges. Get the words exactly right and a whole band of 11+ questions becomes almost automatic. Better still, the nets and 3D-shape questions in the maths paper overlap directly with the cube-net questions in Non-Verbal Reasoning, so the same practice earns marks twice. This guide teaches the properties of 2D and 3D shapes the way GL Assessment tests them, walks through worked examples step by step, and ties every skill to a free downloadable worksheet and a timed on-site mini-mock so your child can prove the skill under exam conditions.
What 11+ geometry (2D and 3D shapes) actually tests
At 11+ level, shape questions are mostly about properties and precise vocabulary rather than long calculation. Children are asked to name polygons, count sides, angles, lines of symmetry, faces, edges and vertices, match a 3D solid to its net, and pick the odd shape out from a row of five. Because GL Assessment now dominates most regions after CEM's separate 11+ tests were phased out around 2022-2023, the format is highly consistent: a diagram, a question, and answers labelled A to E to shade on a separate OMR sheet. Our free worksheet library grades every topic across four tiers — Foundation, Developing, Secure and Greater Depth — so a child enters at their level and climbs.
2D shapes: polygons and their properties
A polygon is any closed 2D shape with straight sides. The number of sides gives the name, and each name carries a set of facts a child should be able to recite instantly.
| Shape | Sides | Key property |
|---|---|---|
| Triangle | 3 | Angles add to 180° |
| Quadrilateral | 4 | Angles add to 360° |
| Pentagon | 5 | Regular = 5 equal sides |
| Hexagon | 6 | Regular = 6 equal sides |
| Octagon | 8 | Regular = 8 equal sides |
The quadrilateral family is the richest source of exam questions, so learn the differences precisely. A square has four equal sides and four right angles. A rectangle has four right angles but only opposite sides equal. A rhombus has four equal sides but its angles are not right angles (think of a "pushed-over square"). A parallelogram has two pairs of parallel sides. A trapezium has exactly one pair of parallel sides, and a kite has two pairs of adjacent equal sides. Triangles are sorted by side length — equilateral (all equal), isosceles (two equal), scalene (all different) — and separately by angle — right-angled, acute or obtuse.
Lines of symmetry: a worked example
A common GL question shows a shape and asks how many lines of symmetry it has. The method is simple: imagine folding the shape so one half lands exactly on the other. Worked example: a regular pentagon. Fold it through each vertex to the middle of the opposite side — that works five times, once per vertex, so a regular pentagon has 5 lines of symmetry. The rule to remember: a regular polygon has as many lines of symmetry as it has sides. A square has 4, an equilateral triangle has 3, and a rectangle (not regular) has only 2. Order of rotational symmetry follows the same count for regular shapes.
3D shapes: faces, edges and vertices
3D solids are tested through counting. A face is a flat surface, an edge is where two faces meet, and a vertex is a corner point. Learn this reference table and most 3D questions become a quick recall.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Square-based pyramid | 5 | 8 | 5 |
| Triangular prism | 5 | 9 | 6 |
| Cylinder | 3 | 2 | 0 |
Nets: the double-value skill
A net is a 2D shape that folds up into a 3D solid. Nets questions appear in the maths paper and, in cube form, in NVR — so this is the single best-value topic to drill. Worked example: "Which net folds to make a cube?" A valid cube net has exactly six squares, and when you mentally fold it, no two squares should overlap and every face must be covered. A quick check: find the square that will become the base, fold the four around it to make the walls, then fold the last one to the top. If two squares would land on the same face, that net is wrong. The classic trap is a net where two squares end up as the same face, leaving a gap elsewhere — always fold the whole thing in your head, not just part of it.
How this appears in a real GL paper
Expect roughly one question a minute in a paper of about 50 questions in 50 minutes, no calculator, answers A-E on a separate OMR sheet. Shape questions reward speed because they are recall-based — a child who knows their vocabulary can bank these marks in seconds and buy time for the harder worded problems. Raw scores are converted to a Standard Age Score (SAS), roughly 69-141 with 100 as average and many grammar schools looking for about 111 or above; the exact mark varies by area and year. Because SAS is age-adjusted, a younger child in the year group is not penalised for their birthday.
Common mistakes and exam traps
- Square vs rhombus: both have four equal sides — the rhombus lacks right angles. Check the angles, not just the sides.
- Counting edges of a solid from a flat picture: hidden edges at the back are easy to miss. Use the table above rather than counting the drawing.
- Miscounting a pyramid's faces: remember the base counts as a face too.
- Regular vs irregular: only regular polygons have equal sides and equal angles; do not assume a hexagon in a diagram is regular.
- Invalid nets: a shape with six squares is not automatically a cube net — always fold it mentally.
Difficulty progression: Year 5 to Year 6
A Year 4/5 version of this skill asks a child to name a shape or count its sides and vertices. The exam-level Year 6 version layers reasoning on top: "Which of these nets will NOT fold into a cube?" or "This shape has 5 faces and 6 vertices — which solid is it?" Build the timeline that way. Start with vocabulary and counting, then move to nets and odd-one-out reasoning by the autumn of Year 5, keeping topics warm with full timed mock papers once they hit Greater Depth.
Download free geometry worksheets
Every 2D and 3D shapes worksheet — with answer keys and OMR sheets — is free in our worksheet library under the Maths tab. No card, no email wall. For exam-style application, the mock library and free papers hub carry the same topic inside full papers, and the GL papers page and revision hub help you tie shape mastery to the wider maths syllabus.
Frequently asked questions
Is a calculator allowed?
No. GL 11+ maths papers are non-calculator throughout, which is why quick recall of shape facts matters so much — you want these marks banked in seconds.
How many shape questions will there be?
It varies by paper, but geometry and shape typically make up a meaningful slice of a 50-question maths paper. Because they are fast recall questions, they are a reliable place to build a strong raw score.
Which year should we start shapes?
Name-and-count work suits Year 4/5, while nets and reasoning questions are best drilled from the autumn of Year 5 so they are secure before Year 6 mocks.