California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

How are lateral faces of a prism defined?

1. They are always triangles

2. They are not parallel to the bases

3. They are parallelograms

4. They cannot be rectangles

The correct answer is: They are parallelograms

The lateral faces of a prism are defined as the faces that connect the two bases of the prism. In a prism, the bases are congruent polygonal shapes that lie parallel to each other. The lateral faces, in contrast, connect these bases and are typically shaped as parallelograms. This characteristic arises from the fact that a prism is formed by translating a polygonal base along a perpendicular height, resulting in lateral faces that maintain the same shape as the base while connecting it to the other base. In most cases, these lateral faces will indeed be parallelograms, including rectangles when the base is a rectangle itself. The other options do not accurately describe lateral faces in a prism. For example, not all lateral faces must be triangles, as prisms with base shapes like rectangles or hexagons will have lateral faces that are parallelograms. While it is true that the lateral faces connect the bases and hence are not parallel to them, this description does not uniquely define the lateral faces, which is why “not parallel to the bases” isn't the best choice. Lastly, while some lateral faces may not be rectangles, it is incorrect to state that they cannot be rectangles; they can be, particularly if the bases are rectangular.