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287_Problem CHAPTER 9 - PROBLEM 9.189 Using the...

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PROBLEM 9.189 Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes. SOLUTION Have ( ) ( ) ( ) 1 2 3 xy xy xy xy I I I I = + + Now, symmetry implies ( ) 1 0 xy I = and for each triangle xy x y I I x yA ′ ′ = + where, using the results of Sample Problem 9.6, 2 2 1 72 x y I b h ′ ′ = − for both triangles. Note that the sign of x y I ′ ′ is unchanged because the angles of
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