Understand the idea.
A net unfolds the surface
A net shows all the surface faces of a solid laid flat and connected along fold edges. To form the solid, the faces must close the surface without overlapping. Having the correct number of faces is necessary, but does not by itself guarantee a valid net.
A cube has six equal square faces. A cuboid has three matching pairs of rectangles. A right triangular prism has two matching triangular ends and three rectangular side faces; each rectangle joins a pair of corresponding triangle edges.
A view shows only one direction
A view looks at an object from one direction. A top view looks straight down; front and side views look horizontally. They show the outline and visible positions from that direction, so other parts can be hidden.
To check a net, hold one face fixed in your imagination and fold adjoining faces around it. Track where every remaining face lands. A net helps construct a surface, while an elevation helps communicate the dimensions seen from one direction.
See the method in action.
Identify a cube net
The diagram has four equal squares in a row, with one square above and one below the second square. Explain why it can make a cube.
Worked solution
- 1
Choose the second square in the row as the base.
It has four edge-neighbours: one on each side in the row, one above and one below.
- 2
Fold those four neighbours up.
They become the four side faces around the base, with no two occupying the same side.
- 3
Fold the far end of the row over the opening.
The remaining square becomes the top face, closing a cube without overlap.
It is a valid cube net.
Describe a prism net
A triangular prism has triangular ends with side lengths 3 cm, 4 cm and 5 cm. The prism is 8 cm long. Describe all faces in a net.
Worked solution
- 1
Identify the two end faces.
A prism has matching cross-sections at its two ends.
- 2
Match each triangle edge to a side rectangle.
The three edge lengths give the widths of the three rectangular faces.
- 3
Use the prism length for every rectangle.
Each rectangle stretches the full eight centimetres between the triangular ends. These are face dimensions, not calculated face areas.
Two matching triangles and rectangles 8 × 3 cm, 8 × 4 cm and 8 × 5 cm.
Try it yourself.
Check your understanding
How many triangular faces and rectangular faces does a triangular prism have?
Show answer & reasoning
2 triangles and 3 rectangles
The prism has two matching triangular ends. Each of the triangle’s three edges extends along the prism to form a rectangle, giving three rectangular faces.
Keep practising
6 worksheet questions · 13 marks
Read the questions online
- Name the solid formed by the net shown.1 mark
- How many faces, edges and vertices does a cube have?3 marks
- A cuboid is 7 cm by 4 cm by 2 cm. List the dimensions of the three pairs of opposite faces.3 marks
- A triangular prism is 10 cm long. Its triangular end has sides 5 cm, 5 cm and 6 cm. List the three rectangular face dimensions.2 marks
- Six equal squares are joined in one straight row. Does counting six faces prove this is a cube net? Explain.2 marks
- Which representation best suits making a cardboard box: a front view or a net? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Name the solid formed by the net shown.1 mark
Six equal square faces fold to form a cube.
Cube - How many faces, edges and vertices does a cube have?3 marks
Count six square surfaces.
Four top, four bottom and four vertical edges total 12.
Four top and four bottom corners total 8.
6 faces, 12 edges and 8 vertices - A cuboid is 7 cm by 4 cm by 2 cm. List the dimensions of the three pairs of opposite faces.3 marks
Each face uses two of the three edge lengths.
Opposite faces are equal rectangles.
Two cm faces; two cm faces; two cm faces - A triangular prism is 10 cm long. Its triangular end has sides 5 cm, 5 cm and 6 cm. List the three rectangular face dimensions.2 marks
Each triangle side is one rectangle width.
All three rectangles extend the 10 cm prism length.
cm, cm and cm - Six equal squares are joined in one straight row. Does counting six faces prove this is a cube net? Explain.2 marks
Faces must fold to cover six different sides without overlap.
A single straight strip cannot cover both the top and bottom while making the four side faces.
No. This arrangement does not close to form a cube. - Which representation best suits making a cardboard box: a front view or a net? Explain.2 marks
A net shows every face and where folds go.
A front view hides the other faces.
A net
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗