You can construct the net of a three-dimensional figure by identifying the shapes that compose each face or surface of the figure and attaching the edges of those shapes to form a new two dimensional object. The Pyramid Arena in Memphis, Tennessee, is a regular right rectangular pyramid, so you can use software to generate the net of a figure like the Pyramid Arena.

Another pyramid-shaped structure is the Rainforest Pyramid at Moody Gardens in Galveston, Texas. Like the Pyramid Arena in Memphis, the Rainforest Pyramid is a right square pyramid whose lateral faces are composed primarily of glass with steel supports to frame the glass panes.

Click on the image below to access an interactive to generate the net for a figure like the Pyramid Arena. Use the drop-list boxes to select Pyramids, and then Regular with Quadrangular Base. Navigate to the Unfold tab and use the slider to unfold the pyramid into a net.

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Conclusion Questions

• How can you identify the base of a pyramid or the bases of a prism in a net of a three-dimensional figure?

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  Need a hint?

  How does the shape of the base(s) in the figure compare to the shape of the base(s) in the net?

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  Check Your Answer

  Once you have identified the base(s) of the three-dimensional figure, look for those same shapes in the net.

• How can you identify the lateral faces of a pyramid or a prism in a net of a three-dimensional figure?

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  What shape would the lateral faces of a pyramid be? What shape would the lateral faces of a prism be?

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  Check Your Answer

  The lateral faces of a pyramid are always triangles. However, the lateral faces of a prism are always parallelograms. Look for those shapes in the net; they should be adjacent to the base(s).

Pause and Reflect

How does a net help to represent the attributes of a three-dimensional figure on a two-dimensional surface?

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Check Your Answer

A net shows you exactly what each face or surface of a three-dimensional figure looks like on a flat plane. It can be used to help construct the figure or to calculate important attributes, such as surface area, of the three-dimensional figure.

Practice

Use the applet in the lesson to help you identify the net for each of the three-dimensional figures shown below.

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Need a hint?

How many faces are present in the net? What shapes are the faces?

1. triangular prism

2. hexagonal pyramid

3. hexagonal prism

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Check Your Answer

1-B
2-D
3-C