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.
There are a few tricks we can use to think about three-dimensional objects represented on a flat surface.
We can never 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 sometimes represent it with its 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 to recover the original shape.
Here is a triangular prism. Move the slider to see its net unfold:
There are many ways to unfold a net from a solid, and in this chapter we will investigate nets of prisms and pyramids.
Here are some prisms:
Prisms have rectangular sides, and the shape on the top and the base is the same. The name of this shape gives the prism its name. Any cross-section taken parallel to the base is always the same.
Here are some pyramids:
Pyramids have triangular sides, and the shape on the base gives the prism its name. Any cross-section taken parallel to the base is always the same shape, but is smaller in size than the base.
Choose the net that folds to give the shape below:
Choose the shape that has the following net:
What three-dimensional shape can be made from these pieces?
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real- world and mathematical problems.