The idea, step by step
A net unfolds the surface
A net lays all the faces of a solid flat, still connected along edges. Folding it must close the solid without two faces occupying the same place. A cube needs six equal square faces. A cuboid also has six rectangular faces, with opposite faces matching. Here we use right prisms: a right triangular prism has two matching triangular ends and three rectangles.
A view shows only one direction
A top view looks straight down; a front or side view looks horizontally. A view does not show every face and may hide parts. A net is useful for making a box, but an elevation is useful for showing its shape from one direction. Label the direction and any dimensions so another person can interpret the drawing.
When checking a net, imagine folding one face at a time around a fixed base. Matching lengths are necessary, but simply counting the faces is not enough: faces may overlap when folded.
A common trap
Calling a top-view sketch a net.
Instead: A view can hide faces. A net must contain every surface face needed to fold the solid.
See the thinking
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.
- The second square can be the base; its four neighbours fold around it.
- The far end of the row becomes the remaining face.
- There are six faces and they close without overlap.
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.
- There are two matching 3–4–5 triangles.
- One rectangle joins each matching pair of triangle sides.
- Each rectangle has length 8 cm, with widths 3 cm, 4 cm and 5 cm.
Check your understanding
How many triangular faces and rectangular faces does a triangular prism have?
Show answer
2 triangles and 3 rectangles
The two ends are triangles; one rectangle joins each of the three pairs of corresponding edges.
Your turn
6 questions · 13 marks · Work at your own pace.
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 7 × 4 cm faces; two 7 × 2 cm faces; two 4 × 2 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.
10 × 5 cm, 10 × 5 cm and 10 × 6 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 ↗