$3.$ Consider the composite shape shown below, composed of three rectangles and symmetric about its vertical axis. The smaller dimension for all three rectangles equals $1$ inch. The longer dimension for each is shown. Round all calclulations to one decimal place.

ension for each is shown. Round all calclulations to one deamar prace.

a$)$ Choose a suitable reference axis and determine the location of the centroid of the shape with respect to your reference axis. Draw the horizontal centroidal axis $\backslash ($ x$-$x $\backslash ).$

b$)$ Determine $\backslash ($ Q$\_\{$x$\}\backslash )$ of the upper rectangle about the centroidal axis.

c$)$ Determine the moment of inertia of the composite shape about its centroidal axis.