Example 4: If the composite area is divided into four individual rectangular pieces as shown, determine the product of inertia of each rectangular piece with respect to its own centroidal horizontal and vertical axes.

Solution:

Since the centroidal horizontal and vertical axes in each rectangle form the axes of symmetry, the product of inertia about these axes would be zero. However, the product of inertia about the centroidal horizontal and vertical axes of the composite shape would not be zero as will be discussed later in the Parallel Axis Theorem Example.