$3$ Cross$-$section Properties

Consider the thin$-$walled beam with the open cross$-$section seen below. The lengths of each portion are

$\frac{?}{\text{b}\text{a}\text{r}}(DE)=100mm\frac{,}{b}ar(EF)=180mm,$ and $\frac{?}{\text{b}\text{a}\text{r}}(FG)=60mm.$ Both the flanges and web have thickness $t=3mm.$

Determine the centroid of the cross section; to make grading easy, what is the location of point E in terms

of the $xy-$coordinate system with origin at the centroid C$?$ Calculate the moments of inertia $I_{},I_{yy},$ and

$I_{xy}.$ Throughout this problem, you may use the thin$-$walled assumption.