Problem # $2$

For the shown area determine:

i$-$ The location of the centroid

ii$-,I_x,I_y,$ and $I_{xy}$ for the given area.

Problem # $3$

Determine the second moment of area, and the product moment of area for the area in problem $2$ with respect to the new centroial axes obtained by rotating the $x$ and $y$ axes $30$ counterclockwise.

Problem # $4$

Determine the orientation of the principal axes at the origin and the corresponding values of moments of inertia for the shape given in problem $2.$