3D shapes & nets
Nets of 3D shapes
A net is what a 3D shape looks like when it is opened out flat. If you cut along the edges of a box and open it up, the flat shape you get is its net. Nets are used to make cardboard packaging.
What is a net?
A net is a flat shape that can be folded up to make a 3D shape. The net shows every face of the shape laid out flat. It can be folded back up again to make the box.
Matching a net to a shape
To find which 3D shape a net makes, look at two things: how many faces it has, and what shape each face is. For example, a net with 1 square and 4 triangles makes a square-based pyramid.
Checking a net folds correctly
If more than one net has the right faces, imagine folding it up. A correct net leaves no gaps and no faces should overlap when it is folded.
Pyramids and prisms
For a pyramid, the number of faces is the number of base sides plus 1: a triangle base gives 4 faces, a square base gives 5 faces, a pentagon base gives 6 faces. A prism has the same shape at both ends with rectangles around the sides.
Worked examples
Identify the net of a square-based pyramid
- A square-based pyramid has 5 faces: 1 square and 4 triangles.
- Look for the net with exactly 1 square and 4 triangles.
Answer: The net with 1 square face and 4 triangular faces makes a square-based pyramid.
Name the shape from a net
- A net is made of 4 triangles only.
- Four triangles fold up into a triangle-based pyramid.
Answer: The net makes a tetrahedron (triangle-based pyramid).
Number of faces of a pyramid
- A hexagon base has 6 sides.
- Number of faces = number of base sides + 1 = 6 + 1.
Answer: A hexagon-based pyramid has 7 faces.
A missing face
- A square-based pyramid net should have 1 square and 4 triangles.
- This net has 1 square and only 3 triangles.
Answer: The missing face is a triangle.
Where you see this in real life
- A cereal box is drawn as a net on card, cut out and folded into a cuboid.
- A triangular sweet packet folds up from the net of a triangular prism.
- Packaging designers draw nets to make boxes with no gaps or overlaps.
- Party hats are made by folding the net of a cone.
Key words
- Net
- A flat shape that folds up to make a 3D shape.
- Face
- A flat surface of a 3D shape, shown flat in the net.
- Tetrahedron
- A triangle-based pyramid with 4 triangular faces.
- Prism
- A 3D shape with the same shape at both ends and rectangles around the sides.