PROBLEM 9.189 Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal xand yaxes. SOLUTION Have ()()()123xyxyxyxyIIII=++Now, symmetry implies ()10xyI=and for each triangle xyx yIIx yA′ ′=+where, using the results of Sample Problem 9.6, 22172x yIb h′ ′= −for both triangles. Note that the sign of x yI′ ′is unchanged because the angles of
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