$(1)$ Required information

$A_1=340mm2,A_2=600mm2$

For the datum axis shown,

$\frac{?}{\text{b}\text{a}\text{r}}(Y{)}_{\text{d}\text{a}\text{t}}=(8\mathrm{.}5A_1+24\mathrm{.}5A_2)\frac{m{m}^3}{A_1+A_2}(m{m}^2)=18\mathrm{.}713(mm)$

Moment of Inertie colculation

The moment of inertia of area $A_1$ about $z$ anis is given as $($:$I_{21}=(\frac{20(17{)}^3}{12}+A_1(10\mathrm{.}213{)}^2)(m{m}^4)=4\mathrm{.}365{10}^{-8}(m{)}^4$