Name & describe prisms & pyramids
Theory
A prism has two congruent, parallel end faces joined by rectangles, and it is named after the shape of those ends (its cross-section). A pyramid has one base and triangular faces that meet at a point, the apex, and it is named after its base. This Year 6 maths page shows how to name prisms and pyramids and count their faces, edges and vertices, including a quick pattern for any number of sides.
A face is a flat surface, an edge is where two faces meet, and a vertex is a corner (plural vertices).
A prism has two congruent, parallel end faces joined by rectangles. Its cross-section (the end shape) is the same all along. A prism with pentagon ends is a pentagonal prism.
A pyramid has one base and triangular faces that meet at the apex. A pyramid with a pentagon base is a pentagonal pyramid.
A prism is named by its ends, not by the face it rests on. The pentagonal prism in the first diagram rests on a rectangle, but it is still a pentagonal prism.
A cube is a rectangular prism whose faces are all squares (a square is a special rectangle).
Counting faces, edges and vertices from the number of sides on the end (prism) or base (pyramid):
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Prism | sides \(+ 2\) | sides \(\times 3\) | sides \(\times 2\) |
| Pyramid | sides \(+ 1\) | sides \(\times 2\) | sides \(+ 1\) |
| Example | F | E | V |
|---|---|---|---|
| Triangular prism | \(5\) | \(9\) | \(6\) |
| Pentagonal prism | \(7\) | \(15\) | \(10\) |
| Triangular pyramid | \(4\) | \(6\) | \(4\) |
| Pentagonal pyramid | \(6\) | \(10\) | \(6\) |
Naming a solid
- Two congruent parallel faces joined by rectangles? It is a prism: name it by those faces.
- One base and triangles meeting at a point? It is a pyramid: name it by the base.
Counting features of a prism
- Faces: one rectangle for each side of the end, plus the \(2\) ends.
- Edges: the sides of both ends, plus one joining edge for each corner: \(3\) times the number of sides.
- Vertices: the corners of both ends: \(2\) times the number of sides.
A pentagonal prism (first diagram).
| \(5 + 2\) | \(=\) | \(7\) |
| \(3 \times 5\) | \(=\) | \(15\) |
| \(2 \times 5\) | \(=\) | \(10\) |
\(7\) faces, \(15\) edges, \(10\) vertices.
(i) How many faces?
(ii) How many edges?
(iii) How many vertices?
| \(8 + 2\) | \(=\) | \(10\) |
| \(3 \times 8\) | \(=\) | \(24\) |
| \(2 \times 8\) | \(=\) | \(16\) |
(i) \(10\)
(ii) \(24\)
(iii) \(16\)
| \(5 + 1\) | \(=\) | \(6\) |
| \(2 \times 5\) | \(=\) | \(10\) |
\(6\) faces, \(10\) edges, \(6\) vertices.
A triangular pyramid: a triangle base and \(3\) triangles meeting at the apex.
A pentagonal prism. A prism is named by its two matching end faces, which are pentagons.
No. It has only one base, and its triangles meet at a point. A prism has two matching ends joined by rectangles.
(i) How many faces?
(ii) How many edges?
(iii) How many vertices?
| \(8 + 1\) | \(=\) | \(9\) |
| \(8 + 8\) | \(=\) | \(16\) |
| \(8 + 1\) | \(=\) | \(9\) |
(i) \(9\)
(ii) \(16\)
(iii) \(9\). A pyramid always has as many faces as vertices.
Common pitfalls
Frequently asked questions
What is a prism?
A solid with two congruent, parallel end faces joined by rectangles.
What is a pyramid?
A solid with one base and triangular faces that meet at a point (the apex).
How are prisms named?
By the shape of their ends, the cross-section: triangular, rectangular, pentagonal, hexagonal ...
How many edges does a pentagonal prism have?
\(15\).
How many faces does a pentagonal pyramid have?
\(6\): the base and \(5\) triangles.