Each triangle in this figure is an isosceles right triangle. The length of \(BD\) is 2 units. What is the number of units in the perimeter of quadrilateral \(ABCD\)? Express your answer in simplest radical form.
BD = 2 Use pythag theorem to find sides ab and ad = sqrt2
then DC = 2
and CB = sqrt 8 soooooo 2 + 2 sqrt2 + sqrt8 = 2 + 4 sqrt2