http://www.ck12.org Chapter 11. Surface Area and Volume
11.2 Cross-Sections and Nets
Here you’ll learn how to view three-dimensional figures in a two-dimensional plane using cross-sections and nets.
What if you wanted to expand your thinking of geometric shapes beyond the flat two-dimensional ones to three
dimensional (3D) ones? In this chapter we are going to expand to 3D. Copy the equilateral triangle to the right onto
a piece of paper and cut it out. Fold on the dotted lines. What shape do these four equilateral triangles make? If
we place two of these equilateral triangles next to each other (like in the far right) what shape do these 8 equilateral
triangles make? After completing this Concept, you’ll be able to answer questions like these.
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Click image to the left for more content.CK-12 Foundation: Chapter11CrossSectionsandNetsA
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Click image to the left for more content.Guidance
While our world is three dimensional, we are used to modeling and thinking about three dimensional objects on
paper (in two dimensions). There are a few common ways to help think about three dimensions in two dimensions.
One way to “view” a three-dimensional figure in a two-dimensional plane, like this text, is to use cross-sections. A
cross-sectionis the intersection of a plane with a solid. Another way to represent a three-dimensional figure in a
two dimensional plane is to use a net. Anetis an unfolded, flat representation of the sides of a three-dimensional
shape.
Example A
What kind of figure does this net create?
The net creates a rectangular prism.
Example B
Draw a net of the right triangular prism below.