Final answer:
The names of the cross-sections of a square pyramid are dependent on the direction and position of the cut. A parallel cut to the base creates a square, a perpendicular cut through the apex forms a triangle, and a slant cut not parallel to the base results in a trapezoid.
Step-by-step explanation:
The student is asking about the names of the shapes formed by the cross-sections of a square pyramid. When you cut a square pyramid parallel to its base, the cross-section is a square.
If the cross-section is taken perpendicular to the base and through the apex, it will be a triangle. If a cut is made parallel to one side of the base but not parallel to the base (slant cut), the cross-section will be a trapezoid (not a rectangle, as rectangles have opposite sides that are parallel, which is not the case in such slant cuts on a pyramid).
A cross-section of a square pyramid will not yield a pentagon unless it has been modified to have a pentagonal base, which is not the standard definition of a square pyramid.