$(30\%)($i$)$ Derive the following geometrical properties $($around $z-$axis that passes though the centroid$)$ of the cross$-$section shown in the figure below, from first principles $($all formulas should be derived as shown in lecture slides, no other method is allowed$)$: elastic section modulus $W_{el}^z,$ plastic section modulus $W_{pl}^z$ and shape factor $k.$ The parameters should be defined as a function of $b_1,b_2,h.$ The cross$-$section is symmetric about the vertical axis that goes through its centroid $(y-$axis$).(25\%)$

$($ii$)$ For the same shape of cross$-$section $(b_1,b_2,h),$ would the geometrical properties around $z-$axis change if it was not symmetric $.$ I $AM$ TIRED $OFAI$ GENERATED REPSONSES!!!! DONT USE $AI!!!!!!!!!!!!$