A 3-dimensional figure has a square base and 4 lateral faces that meet at a point. Explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex.

Answer:

The 3D figure described is a square pyramid. If you make a slice perpendicular to the base that passes through the vertex, the resulting cross section is a triangle. If the slice is perpendicular to the base but does not pass through the vertex, the cross section is a trapezoid.