Glencoe Math: Course 2, Volume 2
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Glencoe Math: Course 2, Volume 2 View details
6. Cross Sections
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Exercise 13 Page 599

Are all the surfaces flat? What does this tell us about whether or not it is a polyhedron? What are the types of polyhedrons?

Figure Name Bases Faces Edges Vertices
Rectangular Prism EHGF, ABCD EHGF, ABCD, ADHE, DCGH, CBFG, ABFE EH, HG, GF, FE, AE, DH, CG, BF, AD, DC, CB, AB A, B, C, D, E, F, G, H
Practice makes perfect

Let's begin by reviewing the definition of a polyhedron.

A polyhedron is a solid composed of all flat surfaces that enclose a single region of space.

Examining the given solid, we can see that it meets this definition.

Therefore, it is a polyhedron. Now, let's consider two types of polyhedrons.

  1. A prism has two parallel congruent bases connected by parallelogram faces.
  2. A pyramid has a polygonal base and three or more triangular faces that meet at a common vertex.

The solid has two parallel congruent bases that are rectangles, so it is a rectangular prism. Let's recall the meaning of the features that we want to identify.

  • Bases are the parallel congruent sides.
  • Faces are any side that forms the polygon.
  • Edges are the line segments connecting the vertices.
  • Vertices are the points where three or more edges intersect.

Now we can name its bases, faces, edges, and vertices.

Bases Faces Edges Vertices
EHGF, ABCD EHGF, ABCD, ADHE, DCGH, CBFG, ABFE EH, HG, GF, FE, AE, DH, CG, BF, AD, DC, CB, AB A, B, C, D, E, F, G, H