2D and 3D shapes and their properties
Pick a shape to see a clear diagram, its properties and an 11+ style question worked through step by step.
Quadrilaterals
Triangles
Polygons
Circles
3D shapes
Quadrilaterals compared
3D shapes compared
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Square-based pyramid | 5 | 8 | 5 |
| Tetrahedron | 4 | 6 | 4 |
| Cylinder | 3 | 2 | 0 |
| Cone | 2 | 1 | 1 |
| Sphere | 1 | 0 | 0 |
| Hemisphere | 2 | 1 | 0 |
Curved faces count as faces here, as most primary schools count them. The cone's apex counts as a vertex.
Shapes in the 11+
Shape questions test properties rather than names: the missing angle in an isosceles triangle, which quadrilateral has one pair of parallel sides, how many edges a prism has. The 11+ maths topics guide shows where shape fits among the other topics, and the maths glossary explains angles, symmetry, area and volume.
Questions parents ask
What is the difference between a 2D and a 3D shape?
A 2D shape is flat, like a drawing on paper, so it has sides but no thickness. A 3D shape is solid, like an object you can hold: it has faces, edges and vertices.
What is a regular polygon?
A flat shape with straight sides where every side is the same length and every angle is the same size. A regular hexagon has six equal sides and six angles of 120°.
How do you work out the angles inside a polygon?
Take away 2 from the number of sides and multiply by 180. A pentagon has (5 − 2) × 180 = 540°. It works because the shape splits into that many triangles from one corner.
Which shapes do children need for the 11+?
Everything in the Key Stage 2 curriculum: triangles, quadrilaterals, polygons up to ten sides, and common 3D shapes, with their angles, symmetry, faces, edges and vertices. Year 6 covers finding missing angles and making nets.
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.