The four particles shown below are connected by rigid rods of negligible mass where y$1=6\mathrm{.}40$ m$.$ The origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with an angular speed of $6\mathrm{.}50$ rad$/$s$.$

Four particles connected by rigid rods in the shape of a rectangle are shown. It lies on an x y$-$coordinate system with the center of the rectangle at the origin. A $2\mathrm{.}00$ kg particle lies in the first quadrant, a $3\mathrm{.}00$ kg particle lies in the second quadrant, a $2\mathrm{.}00$ kg particle lies in the third quadrant and a $4\mathrm{.}00$ kg particle lies in the fourth quadrant. The rods which are parallel to the x$-$axis are of length $4\mathrm{.}00$ m$.$ The rods which are parallel to the y$-$axis are of length y$1$ and are longer than the ones along the x$-$axis.

$($a$)$ Calculate the moment of inertia of the system about the z axis.