Glencoe Math: Course 2, Volume 2
GM
Glencoe Math: Course 2, Volume 2 View details
6. Cross Sections
Continue to next subchapter

Exercise 2 Page 597

Are all the surfaces flat? What does this tell us about whether or not it is a polyhedron? How many bases does the figure have?

Solid Base Faces Edges Vertices
Hexagonal Pyramid RQPONM RQPONM, RQL, QPL, POL, ONL, NML, MRL RQ, QP, PO, ON, NM, MR, RL, QL, PL, OL, NL, ML R, Q, P, O, N, M, L
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 one polygonal base and three or more triangular faces that meet at a common vertex.

The solid has one base that is a hexagon and three triangular faces that meet at the common vertex, so it is a hexagonal pyramid. 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.

Base Faces Edges Vertices
RQPONM RQPONM, RQL, QPL, POL, ONL, NML, MRL RQ, QP, PO, ON, NM, MR, RL, QL, PL, OL, NL, ML R, Q, P, O, N, M, L