Question

PLEASE HELP ME!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a cube at a vertex create? Explain how you know.

Answer 1

A triangle.

Explanation:

As shown above, the plane which slices a corner intersects the polyhedron in
`n` faces which depend on the particular polyhedron.

Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.

Hence the polygon is a triangle.

Answer 2

See below.

Explanation:

There are 3 edges and 3 faces projecting out from a vertex of a cube.

So the polygon produced would be a triangle.