Question

question 8 of 10

all pyramids are platonic solids.

a. true
b. false

Explanation:

Define Platonic solids and pyramids

A Platonic solid is a regular, convex polyhedron where every face is a congruent regular polygon, and the same number of faces meet at each vertex. A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

Identify a counterexample

A square pyramid has a square base and four triangular faces. Because its faces are not all congruent regular polygons (one square and four triangles), and a different number of faces meet at the apex (4 faces) compared to the base vertices (3 faces), it is not a Platonic solid.

Determine the truth value

Since not all pyramids are Platonic solids (only the regular tetrahedron, which is a triangular pyramid with equilateral triangles for all faces, is a Platonic solid), the statement "All pyramids are Platonic solids" is false.

Answer:

• A. True
• B. False (Correct answer)