A cube is a polyhedron. Therefore, no matter how the plane intersects the cube, the result will be a polygon.
Yes, see solution.
Practice makes perfect
We will investigate whether it is possible for a cross section of a cube to be a pentagon. Note that because a cube is a polyhedron, no matter how the plane intersects the cube the result will be a polygon. Therefore, if the plane passes through five faces of the cube, we can have a pentagon.
Keep in mind that there are infinitely many ways to create a pentagon through a cube. Here we are only showing one possibility.
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