Consider the sheet metal cross section shown in $($Figure $1).$ Suppose that

$r=1\mathrm{.}8$ in$.,a=2\mathrm{.}8$ in$.,$ and $b=7\mathrm{.}6$ in$.$

Determine the location $($X$,$Y$)$of the centroid of the sheet metal cross section. Neglect the thickness of the material and slight bends at the corners.