Question

The base of a cube is horizontal. A plane cuts through the cube, creating a pentagon-shaped cross section. The plane is _1_ and may pass through a pair of adjacent _2_ of the base. Options for 1: a.vertical b.slanting Options for 2: a.vertices b.sides

Answer 1

For this problem, imagine a cube laying flat on the floor. If you zoom in on this, it would show a full square. The cutting plane should be able to form a cross-sectional shape of a pentagon. This is a closed figure comprising of 5 sides. The cutting plane should not be vertical. If it was, then it would only for a linear cross section. If it is horizontal, it would superimpose on the square base. So, if the cutting plane is slanting, it would form a pentagon cross section as shown in the right side of the picture attached. Then, it would pass between two adjacent vertices, and three adjacent sides. So, the complete statement would be:

The base of a cube is horizontal. A plane cuts through the cube, creating a pentagon-shaped cross section. The plane is slanting and may pass through a pair of adjacent vertices of the base.