Problem $7(12\%$

The cross$-$sectional area of a T$-$beim is as shown

in Fig. Prob. $7,$

$($a$)$ Locate the centroid of this area, $\frac{?}{\text{b}\text{a}\text{r}}(y).$

$($b$)$ Determine the moment of inertia of this

area about the $y$ axis.

$($c$)$ Determine the moment of inertia of this

area about the centroidal $x^{\text{'}}-x^{\text{'}}$ axis.

$($d$)$ Calculate the moment of inertia about the $x$ axis.

Fig, Prob. $7$