Question

If the cube shown above is sliced by a plane to create a rectangle that is not a square, which sets of vertices could the plane pass through?

Answer 1

To create a non-square rectangle by slicing a cube, one must choose four vertices such that they form two sets of adjacent vertices on two opposing faces, with the second set offset relative to the first.

Step-by-step explanation:

To slice a cube by a plane and create a rectangle that is not a square, one must choose four vertices that do not all belong to the same face and are not all equidistant from each other. If the vertices chosen are equidistant, the result will be a square as all sides will be equal due to the cube's symmetrical properties.

As such, to achieve a non-square rectangle, one could pass the plane through two adjacent vertices on one face and two vertices on the opposing face that are similarly adjacent but offset from the initial pair.

This would create a rectangle with two longer opposite sides and two shorter opposite sides.

Answer 2

Triangle

Step-by-step explanation:

A cube is a three-dimensional figure with six congruent square faces. The cube below is sliced by a plane through vertices 1, 6, and 8.

The cross-section created by the plane is an equilateral triangle.

Therefore, triangle is the best answer.