To determine the shape of the cross section that is perpendicular to a square pyramid, we need to consider the orientation and position of the plane of the cross section relative to the pyramid.
A square pyramid has a square base and triangular faces that meet at a single point called the apex. The shape of the cross section will depend on where the plane intersects the pyramid.
If the plane intersects the pyramid parallel to the base, the cross section will be a square, similar in shape to the base of the pyramid.
If the plane intersects the pyramid along one of the triangular faces, the cross section will be a triangle.
If the plane intersects the pyramid at an angle that cuts across the triangular faces, the cross section will be a polygon with more than three sides, depending on the exact angle of intersection.
In summary, the shape of the cross section perpendicular to a square pyramid can be a square, a triangle, or a polygon with more than three sides, depending on the position and orientation of the plane relative to the pyramid.