Question

which shape or shapes have rectangular faces that are parallel to each other and rectangular faces that are perpendicular to each other?
a. w
b. z
c. w and z
d. x and y

Explanation:

• Shape \(W\): It has non - rectangular faces (the slanted ones), so it does not meet the criteria of having only rectangular faces.
• Shape \(Z\): It has non - rectangular (hexagonal - like) faces, so it does not meet the criteria of having only rectangular faces.
• Shape \(X\) (a cube): A cube is a special case of a rectangular prism. In a cube (and rectangular prism), opposite rectangular faces are parallel. Also, adjacent rectangular faces are perpendicular. For example, in a cube, if we consider the front - back faces (parallel) and the front - top (perpendicular) faces.
• Shape \(Y\) (a rectangular prism): In a rectangular prism, opposite rectangular faces are parallel. And adjacent rectangular faces are perpendicular. For instance, the top - bottom faces (parallel) and the top - front (perpendicular) faces.

Answer:

D. X and Y