The idea, step by step
A net opens a solid
A net is a flat arrangement that can fold to form a solid. Each flat panel becomes a face. Imagine lifting the panels at their shared edges, not stacking them flat on top of each other.
A cube needs six equal square faces. A rectangular prism also has six faces, but they need not all be squares. Opposite faces of a rectangular prism have matching dimensions.
Check the faces and their arrangement
A triangular prism has two matching triangular ends and three rectangular side faces. A square pyramid has one square base and four triangular side faces.
Counting faces is a first check, not a complete test. The pieces must be attached in an arrangement that closes without overlap or gaps. A cylinder uses a rectangle for its curved surface and two equal circular ends.
A common trap
Any collection of six squares is a cube net.
Instead: The arrangement must fold without overlap or gaps. Six squares are necessary for a cube, but not sufficient.
See the thinking
Six equal squares
Which solid can this net make?
- Count the panels: there are six equal squares.
- The four squares in a row can wrap around the sides; the remaining two close the top and bottom.
Two triangular ends
Identify the solid made by the net.
- The two matching triangles form the ends.
- The three rectangles join corresponding sides of those triangles.
Check your understanding
Which solid has one square base and four triangular side faces?
Show answer
A square pyramid.
The four triangles meet above the square base.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Name the solid made by this net.1 mark
- Name this solid.1 mark
- How many triangular faces will this net make?1 mark
- A net has two equal circles and a rectangle for a curved surface. What solid does it make?1 mark
- A rectangular box has length 6 cm, width 4 cm and height 3 cm. List its three pairs of opposite face sizes.3 marks
- Can a cube net contain five squares and one triangle? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Name the solid made by this net.1 mark
The net has six equal squares in a valid folding arrangement.
Cube. - Name this solid.1 mark
Two matching triangular ends join to three rectangular sides.
Triangular prism. - How many triangular faces will this net make?1 mark
Each of the four triangles becomes one sloping face.
Four. - A net has two equal circles and a rectangle for a curved surface. What solid does it make?1 mark
The circles close the ends and the rectangle wraps around.
Cylinder. - A rectangular box has length 6 cm, width 4 cm and height 3 cm. List its three pairs of opposite face sizes.3 marks
Match length/width, length/height and width/height.
Two 6 by 4 cm faces; two 6 by 3 cm faces; two 4 by 3 cm faces. - Can a cube net contain five squares and one triangle? Explain.2 marks
Every cube face is a square, so all six panels must be equal squares.
No.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Connect objects and two-dimensional nets; construct and explain spatial relationships.
Official curriculum source ↗