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Nets of 3-Dimensional Figures

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  • 0:00 A 3-D Figure
  • 0:25 The Net
  • 1:30 Counting the Faces
  • 1:55 Example
  • 2:25 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to deconstruct a 3-dimensional figure into its 2-dimensional net. Learn what kind of shape you will get after opening and flattening your 3-dimensional figure.

A 3-D Figure

In this lesson, we will look at 3-dimensional figures and what kind of shapes we get if we open up our 3-dimensional figure and lay it out flat on the floor. A 3-dimensional figure is a solid that we can hold. For example, this is a 3-dimensional figure. It is a rectangular brick that we can pick up and hold.

net

If we cut some of the edges so we can open up this shape and lay its sides flat on the ground, we would be looking at its net.

The Net

The net is a pattern we can cut out and fold to create a 3-dimensional figure. For our rectangular brick, the net looks like this:

net

Looking at this net, we see that the two tabs that are sticking out on the sides make up the small sides of the brick. The other sides with the longer rectangles make up the sides that go around. Is it possible to get a different net that represents the same rectangular brick? Yes! The two tabs can be located anywhere along the sides. They could be connected to the bottom long rectangle or the second one on top of that one or even the very top rectangle.

Most nets will have dotted lines or some other line to show you where the bends are. It is very similar to origami instructions that show you where to fold the paper. It does take some imagination to visualize what kind of shape you will get by folding the net if you don't already know the shape. One of the best ways to practice this kind of visualization is to cut out the net and fold it on the lines to see what kind of shape you end up with.

Counting the Faces

Because the net is made up of all the sides of our 3-dimensional figure, we can also count the number of faces of our 3-dimensional figure from its net. Looking at our net, we can see that the rectangular brick has a total of six faces, or six sides. We have the four longer rectangles and then the two smaller rectangles on the sides.

Example

Let's look at another example. What kind of shape do you get from folding this net?

net

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