A beam has the special extruded cross$-$section shown in Figure Q$2.$ From the dimensions

given, determine:

i$)$ the position of the centroid;

ii$)$ the $2^{nd}$ moment of area about the x and y axes;

iii$)$ the product $2^{nd}$ moment of area;

iv$)$ the angle of inclination of the principal axes;

v$)$ the principal $2^{nd}$ moments of area, analytically and graphically.