3D objects: polyhedra, prisms and pyramids
Polyhedra and objects with curved surfaces, the rule for prisms and pyramids, Euler’s formula and nets that fold into a cube. Read one step, play with it, then tap “I understand this”.
Polyhedron or not?
A polyhedron is a 3D object with only flat faces and straight edges. A cylinder, cone and sphere have a curved surface, so they are not polyhedra.
The 3D cards
Choose an object and read its properties.
Sort it
Is it a polyhedron?
Correct: 0The rule for prisms and pyramids
If the base has n sides, you can work everything out without counting:
| Faces | Edges | Vertices | |
|---|---|---|---|
| Prism | n + 2 | 3n | 2n |
| Pyramid | n + 1 | 2n | n + 1 |
Build a prism or pyramid
Choose prism or pyramid and change the sides of the base.
There is one rectangle for every side of the base (n rectangles), plus the two bases themselves at the top and bottom.
Euler’s formula
For every polyhedron: faces + vertices − edges = 2 (F + V − E = 2). If you know two of the three, you can work out the third.
Count fast
Use the rule or Euler’s formula.
Correct: 0Imagine building the polyhedron one edge at a time. Every new edge brings either a new vertex or a new face, so faces + vertices − edges never changes. For a cube: 6 + 8 − 12 = 2.
Nets
A net is the flat pattern that folds into a 3D object. A cube has 11 different nets of 6 squares.
Does it fold into a cube?
Decide, then see where each square lands.
Correct: 0Whose net is this?
Choose the object this net makes.
Correct: 0A cube has 6 different faces. If two squares land on the same face when you fold, another face stays open.
Check yourself
- A polyhedron has only flat faces; a cylinder, cone and sphere are not polyhedra.
- Prism with n sides in the base: n + 2 faces, 3n edges, 2n vertices.
- Pyramid: n + 1 faces, 2n edges, n + 1 vertices.
- Euler: F + V − E = 2 for every polyhedron.
- A cube has 11 different nets.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 4 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 3 A4 pagesPractice sheet
- Paper 17 pages · PDFPaperMemo
Ready for more? The Grade 7 geometry quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Make a cube or pyramid out of paper together: draw the net, cut it out and fold. Then count the faces, edges and vertices and test Euler’s formula.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.