What are the shapes of the horizontal

cross sections of a right rectangular pyramid? What
are the shapes of vertical cross sections through
the vertex opposite the base?

The shapes of the horizontal cross sections of a right rectangular pyramid are rectangles. This is because each cross section is parallel to the base of the pyramid and perpendicular to its height.

The shapes of vertical cross sections through the vertex opposite the base would vary depending on the angle at which the section is taken. These cross sections could be triangles, trapezoids, or even irregular shapes, depending on the angle of the cut.