Engineering Mechanics Practice Exam

The concept being tested is the parallel axis theorem for area moments of inertia. When you find the moment of inertia about an axis parallel to the centroidal axis, you add a term that accounts for shifting the axis by distance d. That extra term is the area times the square of that distance: A d^2. So the relation is I_about_axis = I_centroid + A d^2. The correct completion reflects this A d^2 term. The other options would introduce incorrect linear or mixed terms, or involve squaring the area itself, which do not match the established relation.