Understand the idea.
Count the folded object
On a solid with flat polygon faces, a face is a flat surface, an edge is a shared side between faces and a vertex is a corner where edges meet. Count the finished solid.
Folding joins some separate net corners and boundary segments together. Counting them before folding can count the same solid feature more than once. A cube has six faces, twelve distinct edges and eight vertices.
Use shape and position clues
Use face shapes as well as counts when identifying solids. A triangular prism and a square pyramid each have five faces, but one has two triangles and the other has four.
Even matching feature counts may not identify a shape completely. A cube and a rectangular box that is not a cube both have six faces, twelve edges and eight vertices. Face dimensions and equal-length information distinguish them.
See the method in action.
Count shared edges
Why does a cube have 12 edges rather than 24?
Worked solution
- 1
Count the edge appearances on all faces.
Each of the six square faces has four sides to count.
- 2
Account for sharing.
Every cube edge belongs to two faces, so the face-by-face count includes every edge twice.
- 3
Find the distinct edges.
Dividing by two removes the duplicate appearance of each physical edge.
12 edges.
Five faces is not enough
A solid has five faces. Must it be a triangular prism?
Worked solution
- 1
Describe the prism face group.
A triangular prism has two triangular ends and three rectangular side faces.
- 2
Give another five-face solid.
A square pyramid has one square base and four triangular sides.
- 3
Decide what the count can establish.
The square pyramid is a counterexample: five faces do not force a solid to be a triangular prism. Face shapes are also needed.
No; the face shapes are also needed.
Try it yourself.
Check your understanding
Which has more vertices: a cube or a square pyramid?
Show answer & reasoning
A cube.
The square pyramid has four base vertices and one apex, giving . A cube has eight vertices, so the cube has more.
Keep practising
6 worksheet questions · 10 marks
Read the questions online
- State the faces, edges and vertices of a cube.3 marks
- A square pyramid has four base edges and four edges from the base corners to the apex. How many edges?1 mark
- A triangular prism has two triangular ends. Count its vertices.1 mark
- A solid has five faces: two triangles and three rectangles. Name it.1 mark
- Can a cube and a rectangular prism have the same face, edge and vertex counts? Explain.2 marks
- In the labelled cube net, will faces B and D touch along an edge after folding? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- State the faces, edges and vertices of a cube.3 marks
Count the folded solid; each edge is shared by two faces.
6 faces, 12 edges, 8 vertices. - A square pyramid has four base edges and four edges from the base corners to the apex. How many edges?1 mark
.
8 edges. - A triangular prism has two triangular ends. Count its vertices.1 mark
Each end has 3 corners; .
6 vertices. - A solid has five faces: two triangles and three rectangles. Name it.1 mark
The matching triangular ends are joined by three rectangular sides.
Triangular prism. - Can a cube and a rectangular prism have the same face, edge and vertex counts? Explain.2 marks
Both have 6 faces, 12 edges and 8 vertices. Equal edge lengths distinguish a cube.
Yes. - In the labelled cube net, will faces B and D touch along an edge after folding? Explain.2 marks
They become opposite faces of the cube.
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 ↗