Question

using the piling method, which of the following can be constructed from polygons alone? check all that apply. a. prism b. circle c. cone d. cylinder e. pyramid (not including the vertex) f. pyramid (including the vertex)

Explanation:

• A prism can be constructed by piling congruent polygons (the bases) and rectangles (the lateral faces).
• A cylinder has circular bases (not polygons) so it cannot be constructed from polygons alone.
• A cone has a circular base (not a polygon) so it cannot be constructed from polygons alone.
• A pyramid (including the vertex) has a polygonal base but the triangular faces meet at a non - polygonal vertex point (in 3D space, the vertex is a single point, not a polygon). A pyramid (not including the vertex) still has triangular faces which are polygons, but the vertex is a key part of the pyramid's definition in 3D. However, if we consider just the base and the lateral faces (as polygons), a prism is more straightforwardly constructed from polygons.

Answer:

A. Prism