To determine the shapes that can be formed by the intersection of a plane and a square pyramid, we need to consider the different ways in which the plane can intersect the pyramid:
1. Square:
- When the intersection plane is parallel to the base of the square pyramid and passes through the region where the cross section remains a square, the resulting cross section will be a square.
2. Triangle:
- When the intersection plane cuts through only three of the edges of the pyramid, it results in a triangular cross section. This can occur if the plane slants in such a way that it meets only three edges.
3. Trapezoid:
- If the intersection plane is not parallel to the base but intersects two opposite edges and two non-opposite edges, it forms a trapezoidal cross section.
4. Non-square Rectangle:
- When the intersection plane is parallel to the base but at a different height, it can produce a rectangular shape that is not necessarily a square. This happens when the plane does not pass through the apex or the base directly but slices through the sides of the pyramid.
Given these possible outcomes, the shapes that a cross section can take when intersecting a square pyramid with a plane are:
- Square
- Triangle
- Trapezoid
- Non-square rectangle
Thus, the three correct options from the provided list are:
- Square
- Triangle
- Trapezoid
