The MI of the rod AB(I1 )and CD(I2 ) about the axis PQ( as shown in the figure ) are same.
I1=I2=ML212
The MI of the rod BC(I3 )and AD(I4 ) about the axis PQ( as shown in the figure ) are same..
I3=I4=M(L2)2
AD||PQ and BC||PQ and all points on AD are at same distance from the axis PQ, all points on BC are at same distance from the axis PQ,
∴I=I1+I2+I3+I4=2×ML212+2×M(L2)2=23ML2