Answer: The slices you described, a triangle parallel to the base and a rectangle perpendicular to the base, indicate that the three-dimensional shape being sliced is a rectangular prism.
A rectangular prism is a solid geometric figure with six rectangular faces. It has two parallel and congruent rectangular bases and four rectangular lateral faces. When a rectangular prism is sliced parallel to one of its bases, the resulting slice is a rectangle. When it is sliced parallel to one of its lateral faces, the resulting slice is a parallelogram.