What is a pyramid?
A pyramid is a 3D shape with a flat base and triangle faces that meet at a point at the top.
The answer
For a pyramid whose base has n sides: n + 1 faces, 2 × n edges and n + 1 vertices. A square-based pyramid has 5 faces, 8 edges and 5 vertices.
Pyramid diagram and properties
| Property | Count |
|---|---|
| Faces1 square and 4 triangles on the square-based pyramid drawn | 5 |
| Flat faces | 5 |
| Curved faces | 0 |
| Edges | 8 |
| Vertices (corners) | 5 |
Key facts about the pyramid
- A pyramid is named after its base: a square-based pyramid, a triangular-based pyramid, a pentagonal-based pyramid.
- There is one triangle face for every side of the base.
- The point at the top is called the apex. It is one of the vertices.
- A triangular-based pyramid is also called a tetrahedron. All four of its faces are triangles.
Faces, edges and vertices of pyramids
For a pyramid whose base has n sides: faces = n + 1, edges = 2 × n, vertices = n + 1. Every row passes Euler's check: vertices − edges + faces = 2.
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Triangular-based pyramid (tetrahedron) | 4 | 6 | 4 |
| Square-based pyramid | 5 | 8 | 5 |
| Pentagonal-based pyramid | 6 | 10 | 6 |
| Hexagonal-based pyramid | 7 | 12 | 7 |
Where you see it
The Great Pyramid of Giza is a square-based pyramid. So is the glass pyramid outside the Louvre in Paris.
The common mistake
Forgetting to count the base as a face. A square-based pyramid has 5 faces: 4 triangles and the square it stands on.
An 11+ style question
A pyramid has 7 faces. How many edges does it have?
Answer: 12 edges
- A pyramid has 1 base face plus one triangle for every side of the base.
- 7 − 1 = 6 triangles, so the base has 6 sides: it is a hexagonal-based pyramid.
- It has 6 edges round the base and 6 going up to the apex: 6 + 6 = 12.
Related shapes and skills
More shapes
Questions parents ask
How many faces, edges and vertices does a pyramid have?
It depends on the shape of its base. For a pyramid whose base has n sides: n + 1 faces, 2 × n edges and n + 1 vertices. A square-based pyramid has 5 faces, 8 edges and 5 vertices. The same counting works for any pyramid: a pentagonal-based pyramid has 5 + 1 = 6 faces, 2 × 5 = 10 edges and 5 + 1 = 6 vertices.
Is a cone a pyramid?
No. A cone has a circular base and a curved face, and a pyramid has a flat base with straight sides and flat triangle faces. They both come to a point, which is why they are often compared.
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.