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Determine the $y-$coordinate of the centroid of the shaded composite area.

Given $a=32mm$;$b=192mm$ and $d=224mm.$

A$.y^{\text{'}}=121\mathrm{.}60mm$

B$.y^{\text{'}}=156\mathrm{.}80mm$

C$.y^{\text{'}}=129\mathrm{.}44mm$

D$.y^{\text{'}}=135\mathrm{.}89mm$

$y^{\text{'}}=144\mathrm{.}00mm$

$?$