Locate the centroid $\frac{?}{\text{b}\text{a}\text{r}}(y)$ of the cross$-$sectional area of the beam constructed from a channel and a plate. Assume all corners are square and neglect the size of the weld at $A.$ Take $a=340mm,b=370mm.$

$($Figure $1)$

Express your answer to three significant figures and include the appropriate units.

$\frac{?}{\text{b}\text{a}\text{r}}(y)=$

$20$ mm y$10$ mm$70$ m