When a slice is made parallel to the base of a right rectangular pyramid that has four equal edges, the resulting cross-section will be similar in shape to the base of the pyramid. Since the base of the pyramid is a rectangle, the cross-section will also be a rectangle.
However, since the options provided do not include rectangle, and given the fact that all edges of the pyramid are equal, the pyramid can be categorized as a square pyramid (where the base is a square).
So, when you slice parallel to the base, the shape of the cross section is a square.
Therefore, the correct answer is:
square