Question

If a plane that is neither parallel nor perpendicular to base B passes through the cube, which of the following could be the shape of the intersection of the plane and the cube.

a) A parallelogram with diagonal equal to diagonal of B

b) A parallelogram with diagonal greater than the diagonal of B

c) A parallelogram with diagonal less than the diagonal of B

d) A square with side length equal to the side length of the cube

Answer 1

The intersection of the plane and the cube, if the plane is neither parallel nor perpendicular to the base, could be a parallelogram.

Step-by-step explanation:

The intersection of the plane and the cube, if the plane is neither parallel nor perpendicular to the base, could be a parallelogram.

To understand why, imagine slicing through the cube with the plane. The resulting intersection will have four sides, with opposite sides being parallel to each other. These properties make it a parallelogram.

The shape of the parallelogram could have various sizes and angles, so it could be a, b, or c, but not d.