Nets of prisms & pyramids
Theory
A net is a solid opened out flat, so every face is shown once, joined edge to edge. Counting the shapes in a net counts the faces: a rectangular prism has \(6\) rectangles, a square pyramid has \(1\) square and \(4\) triangles.
A net is a solid opened out flat, so that every face is shown once, joined edge to edge.
Each flat shape in the net becomes one face when the net is folded up. Nothing is added or lost.
A prism has two matching end faces joined by rectangles; a pyramid has one base with triangles rising to a point.
Count the shapes in a net to count the faces of the folded solid. Each shape becomes one face.
| Solid | Net is made of | Faces |
|---|---|---|
| Rectangular prism | \(6\) rectangles | \(6\) |
| Triangular prism | \(2\) triangles, \(3\) rectangles | \(5\) |
| Square pyramid | \(1\) square, \(4\) triangles | \(5\) |
| Triangular pyramid | \(4\) triangles | \(4\) |
How to read a net
- Count the flat shapes; each one becomes a face.
- Sort them into rectangles, squares and triangles.
- Match the shapes to a solid: two matching ends means a prism; one base with triangles means a pyramid.
- Fold the net in your mind along the shared edges to check it closes with no gaps.
Each rectangle becomes one face.
| \(4 + 1 + 1\) | \(=\) | \(6\) |
The solid has 6 faces.
| \(2 + 3\) | \(=\) | \(5\) |
The two triangles are the ends, so it is a triangular prism.
| \(1 + 4\) | \(=\) | \(5\) |
The square is the base and the four triangles meet at the apex, so 5 faces.
| \(6 \div 2\) | \(=\) | \(3\) |
They form three matching pairs: front and back, top and base, left and right.
Common pitfalls
Frequently asked questions
What is a net?
A net is a solid opened out flat so every face is shown once, joined edge to edge. Folding it back up rebuilds the solid.
How many faces does a rectangular prism have?
Six. Its net is six rectangles that form three matching pairs: front and back, top and base, left and right.
What does the net of a square pyramid look like?
A square base with a triangle joined to each of its four sides. That is \(1 + 4 = 5\) faces.
How do you tell a prism from a pyramid?
A prism has two matching end faces joined by rectangles. A pyramid has one base and triangles that rise to meet at a point.
How many triangles are in the net of a triangular prism?
Two. They are the two ends. Three rectangles wrap around to join them, giving five faces in total.