help question

$P$  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  $ABCDP?$