Question
Two uniform thin identical rods, each of mass M and length L, are joined so as to form a cross as shown in Fig. What is the moment of inertia of the system about the bisector line AB? 
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Answer
Take a bisector line A'B' perpendicular to bisector line AB. Moment of inertia about an axis perpendicular to the plane and passing through the point of intersection is $2\times\frac{\text{ML}^2}{12}\text{ or }\frac{\text{ML}^6}{6}$ Applying theorem of perpendicular axis, we get $\frac{\text{ML}^2}{6}=\text{I}_{\text{AB}}+\text{I}_{\text{AB}'}$ $\text{or }2\text{I}=\frac{\text{ML}^2}{12}\text{ or }\text{I}=\frac{\text{ML}^2}{12}$
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