Question

determine whether the solid is a polyhedron. then identify the solid. if it is a polyhedron, name the bases, faces, edges, and vertices.
the figure is
select choice
it is a
select choice
.
bases:
select choice
faces:
select choice
edges: $overline{de}$, $overline{ef}$, $overline{fg}$, $overline{gd}$, $overline{dh}$, $overline{ej}$, $overline{fk}$, $overline{gl}$, $overline{hj}$, $overline{jk}$, $overline{kl}$, $overline{lh}$
vertices:
select choice
the cone and pyramid have nearly the same volumes
the cone has a much greater volume
the pyramid has a much greater volume

Explanation:

Step1: Identify if it's a polyhedron

A polyhedron is a solid with flat polygonal faces, straight edges, and vertices. The given figure (a prism-like shape with rectangular faces) has all flat faces, so it is a polyhedron.

Step2: Name the solid

The figure is a rectangular prism (or a cuboid). Bases: Two congruent rectangular faces (e.g., \( \square DEFG \) and \( \square HJKL \)). Faces: All 6 rectangular faces (e.g., \( \square DEFG \), \( \square EFKJ \), \( \square FKL G \), \( \square GLHD \), \( \square LHJD \), \( \square DEJH \)). Edges: All the line segments connecting vertices (e.g., \( \overline{DE} \), \( \overline{EF} \), \( \overline{FG} \), \( \overline{GD} \), \( \overline{DH} \), \( \overline{EJ} \), \( \overline{FK} \), \( \overline{GL} \), \( \overline{HJ} \), \( \overline{JK} \), \( \overline{KL} \), \( \overline{LH} \)). Vertices: \( D, E, F, G, H, J, K, L \).

Step3: Confirm the type

Since it has two congruent rectangular bases and rectangular lateral faces, it's a rectangular prism (a type of polyhedron).

Answer:

The solid is a polyhedron. It is a rectangular prism.
Bases: Two congruent rectangular faces (e.g., \( \square DEFG \) and \( \square HJKL \)).
Faces: 6 rectangular faces (e.g., \( \square DEFG \), \( \square EFKJ \), \( \square FKL G \), \( \square GLHD \), \( \square LHJD \), \( \square DEJH \)).
Edges: Segments like \( \overline{DE} \), \( \overline{EF} \), \( \overline{FG} \), \( \overline{GD} \), \( \overline{DH} \), \( \overline{EJ} \), \( \overline{FK} \), \( \overline{GL} \), \( \overline{HJ} \), \( \overline{JK} \), \( \overline{KL} \), \( \overline{LH} \).
Vertices: \( D, E, F, G, H, J, K, L \).