Nets of prisms & pyramids
Theory
A net is a 3D object opened out flat so that every face can be seen. Folding the net back up makes the object again. This Year 5 maths page shows the nets of prisms and pyramids, how to count the faces in a net, and how to check that a set of shapes will fold up into the solid you want.
A net is a flat shape that folds up to make a 3D object. Every face of the object appears once in the net.
A prism has two matching ends joined by rectangles. A rectangular prism (a box) has \(6\) rectangular faces; a cube has \(6\) equal squares; a triangular prism has \(2\) triangles and \(3\) rectangles.
A pyramid has one base, and triangles that meet at a point called the apex. A square pyramid has \(1\) square and \(4\) triangles; a triangular pyramid has \(4\) triangles.
The faces of a rectangular prism come in three matching pairs: top and bottom, front and back, left and right.
A solid can have several different nets. A net only works if no two faces overlap when it is folded.
Faces in the net of each solid:
| Solid | Shapes in the net | Faces |
|---|---|---|
| Cube | \(6\) equal squares | \(6\) |
| Rectangular prism | \(6\) rectangles (\(3\) pairs) | \(6\) |
| Triangular prism | \(2\) triangles, \(3\) rectangles | \(5\) |
| Square pyramid | \(1\) square, \(4\) triangles | \(5\) |
| Triangular pyramid | \(4\) triangles | \(4\) |
Name the solid from a net
- Count the faces.
- Look at the shapes: two matching end shapes joined by rectangles means a prism; one base and triangles means a pyramid.
- Name the prism or pyramid after its end or base shape.
Check a set of rectangles for a box
- Group the rectangles by size.
- Check there are three pairs.
- Check the pairs share edges: a box \(l\) by \(w\) by \(h\) needs \(l \times w\), \(l \times h\) and \(w \times h\) rectangles.
Its rectangles are \(4\) by \(3\), \(4\) by \(2\) and \(3\) by \(2\), two of each, so it folds into a box \(4\) long, \(3\) wide and \(2\) high.
A triangular pyramid (one triangle is the base, three meet at the apex).
(i) How many rectangles are in its net?
(ii) What sizes are they?
(i) \(6\)
(ii) Two \(9\) by \(6\), two \(9\) by \(2\) and two \(6\) by \(2\)
Yes. There are three pairs, and they fit a box \(10\) by \(4\) by \(1\).
No. The three sizes do not share edges: the last pair would need to be \(3\) cm by \(5\) cm.
(i) What solid does it make?
(ii) How many faces does the solid have?
(i) A pentagonal pyramid
(ii) \(6\) faces
| \(2 \times 8 + 2 \times 12 + 2 \times 6\) | \(=\) | \(52\,\text{cm}^2\) |
\(52\,\text{cm}^2\) of card.
The two triangular ends. The net has \(5\) faces.
Common pitfalls
Frequently asked questions
What is a net?
A flat shape that can be folded to make a 3D object, showing every face once.
How many faces does the net of a rectangular prism have?
\(6\) rectangles, in three matching pairs.
What does the net of a triangular prism look like?
Three rectangles in a row with a triangle on each end: \(5\) faces.
How is a pyramid net different from a prism net?
A pyramid net has one base with triangles around it. A prism net has two matching ends joined by rectangles.
Does a cube have only one net?
No. There are \(11\) different nets of a cube.