Construction of Polygons and Nets for Cuboids and Prisms
Primary 6 · Mathematics
Construction of Polygons and Nets for Cuboids and Prisms
Lesson 5 of 5
18 min
Let's begin
Uwase bought a bar of soap at the shop in her umudugudu. At home she carefully opened the empty box along its glued edges and pressed it flat. To her surprise, the whole box was one piece of card, with no extra bits.
That flat piece of card is called a net. In this lesson you will learn to recognise, draw and use nets of cubes, cuboids and prisms.
A face is a flat surface, an edge is where two faces meet, and a vertex is a corner where edges meet.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| cube | 6 | 12 | 8 |
| cuboid | 6 | 12 | 8 |
| triangular prism | 5 | 9 | 6 |
| pentagonal prism | 7 | 15 | 10 |
| hexagonal prism | 8 | 18 | 12 |
| square-based pyramid | 5 | 8 | 5 |
A prism has two identical, parallel ends (the bases) joined by rectangles. It is named after the shape of its base. If the base has n sides, the prism has n + 2 faces, 3 × n edges and 2 × n vertices.
A neat check that works for all these solids: faces + vertices − edges = 2. For a cube: 6 + 8 − 12 = 2.
A net is a flat pattern that folds up to make a solid. It shows every face exactly once.
Uwase's soap box is a cuboid 5 cm long, 3 cm wide and 2 cm high. Its net has three pairs of matching rectangles:
Because the net shows every face once, adding up the areas of its rectangles gives the surface area of the box.
A cube's net is made of 6 equal squares. There are 11 different arrangements that fold into a cube. The best known is a cross: a row of four squares, with one square above and one below the second square. But not every arrangement works. A block of 2 rows of 3 squares cannot fold into a cube, and no cube net ever has four squares forming a 2-by-2 block.
A triangular prism has 2 triangular ends and 3 rectangular sides, so its net has 2 triangles and 3 rectangles. In the net below the rectangles are squares, because the prism is as long as the sides of its triangles.
Tip
Count in pairs for a cuboid: top and bottom, front and back, left and right.
For any prism: 2 bases, plus one rectangle for every side of the base.
Answers
What you learned today
Sources and credits
The soap-box story, the cuboid net drawing, the table of faces, edges and vertices and the worked examples were written by Ganzaa.
Quick check
How many faces does a pentagonal prism have?
