Topics
12. Geometry
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AustraliaNSW
Stage 3

12.06 Nets of solids

Lesson
Practice
Lesson

Are you ready?

Let's review features of  3D objects  to help us in this lesson.

Examples

Example 1

Here is a rectangular prism.

An image of a rectangular prism.
a

How many faces does it have?

Worked Solution
Create a strategy

Faces are the flat sides of a solid.

Apply the idea

It has 6 faces.

b

How many vertices does it have?

Worked Solution
Create a strategy

Vertices are the corners where edges meet.

Apply the idea

It has 8 vertices.

c

How many edges does it have?

Worked Solution
Create a strategy

An edge is the line where two faces meet.

Apply the idea

It has 12 edges.

Idea summary

A prism can be made with any polygon at its base.

Nets of solids

Let's look at how to make 2D representations of 3D solid objects.

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Examples

Example 2

Choose the net that folds to give the shape below:

An image of a rectangular prism.
A
The image shows a net of a solid. Ask your teacher for more information.
B
The image shows a net of a solid. Ask your teacher for more information.
C
The image shows a net of a solid. Ask your teacher for more information.
D
The image shows a net of a solid. Ask your teacher for more information.
Worked Solution
Create a strategy

Choose the net with the same number of faces as the solid and can be folded along its edges to make the solid.

Apply the idea

The solid has 6 rectangular sides, where the opposite sides are the same.

Looking at the options, we can see that options C and D have 6 rectangles.

If we folded option D then the opposite rectangles would be the same. This is not true for option C.

So the correct answer is Option D.

Idea summary

When we make a net of a solid, there may be more than one possibility. We can use the edges and vertices to help us, as well as the two dimensional (2D) shapes.

Outcomes

MA3-14MG

identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

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