\(P\) is the midpoint of \(\overline{BD}\) . \(AP = BP = 4\) , \(\overline{AP} \perp \overline{BD}\) , \(\overline{BD} \perp \overline{DC}\) , \(\overline{AB} \perp \overline{BC}\) . In simple radical form,

what is the perimeter of pentagon \(ABCDP?\)