Question

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 1

Answer:

Given is -

A 3-dimensional figure has a square base and 4 lateral faces that meet at a point. This shows that the figure is a square pyramid.

When a square pyramid is cross sectioned perpendicular to the base and through the vertex , the resulting shape will be a triangle.

When a slice is made perpendicular to the base and not through the vertex, the resulting shape will be a trapezoid.

In square pyramids and rectangular pyramids also, the cross sections formed by slicing perpendicular to the base through two opposite sides of the base but not through the vertex, will be trapezoids.

Answer 2

The figure is a square pyramid. A slice made perpendicular to the base and through the vertex creates a cross section with the shape of a triangle. A slice made perpendicular to the base and not through the vertex is a trapezoid.