7.05 Nets of solids
Introduction
Three-dimensional objects are represented on two-dimensional surfaces all the time. Screens, whiteboards, paper, and other flat surfaces can create the illusion of depth when displaying a picture of something.
Let's explore how to name three-dimensional objects and then visualize them by representing them on a two-dimensional, or flat surface.
Naming three-dimensional objects
Prisms have rectangular sides, and two bases that are the same shape. The name of this shape gives the prism its name.
Pyramids have triangular sides, and one base that gives the pyramid its name.
When naming the solid, state the name of the base first then if it is a prism or pyramid. Let's try naming one in the following worked example.
Examples
Example 1
Name the solid.
We use the shape of the sides to identify if the solid is a prism or pyramid. We use the shape of the base to name the pyramid or prism.
Nets
We cannot see every part of a three-dimensional object at once - there is always part of it that is behind the view we are looking at. To better think about a solid object we can represent it with a net. Each face of the solid is laid flat on the same surface, breaking it along the edges and folding it out. This way we can think about folding it back up along its edges back to the original shape.
Exploration
This is a triangular prism. Move the slider to see unfold and see the net:
What is the composition of the net of the triangular prism above?
There are many ways to unfold a net from a solid, and in this chapter we will investigate nets of prisms and pyramids.
Examples
Example 2
Choose the net that folds to give the shape below:
Example 3
Choose the shape that has the following net:
A net is the 2D version of a solid. It can be shown by unfolding the edges of a solid.