Verified answer

You can obviously get a triangle (not one of the choices) cutting parallel to the triangular faces (or at an angle).

You can also get a rectangle (as you noted) by cutting parallel to a rectangular face.

Since the ends are parallel, if you cut from one triangular face to the other, but *not* parallel to a rectangular face, the result will be a trapezoid.

There is no way to slice through 6 separate edges to get the vertices of a hexagon.

Answer:

a) Rectangle

b) Trapezoid

If you slice through its triangular cross section it could be B a trapezoid.

Assuming the "slicing" is done by a plane.

All rectangles are trapezoids, right?

Can you make a non-rectangular trapezoid also? Yes. Just make a rectangle and rotate about a side on the triangular face.

Hexagon is not possible as there are only 5 faces (each face can make at most one edge when cut with another plane).

Also possible are triangles, some irregular quadrilaterals, and pentagons.

Any section cutting three faces is a triangle. There are many ways to effect that.

If it is a right prism, then a section parallel to one of the lateral faces is a rectangle.

Each side of the section is the intersection of the cutting plane and a face of the given solid. The solid has only five faces, so a hexagonal section is not possible.

Follow-up:

I beg your pardon. That second case calls for a trapezoid, not necessarily a rectangle. In that case, let the cutting plane intersect both bases and only two of the lateral faces. It intersects the bases on parallel line segments, so the section is a trapezoid. It is not necessary for it to be a right prism.