Height of point P above a rectangle

Given a rectangle with points ABCD.

The lengths AB, BC, CD, and DA are all known.

(AB=CD and BC=DA).

Given a point P that is not coplanar with rectangle ABCD.

The distance from point A to P is a, where a is unknown.

The distance from point B to P is a+b, where b is known.

The distance from point C to P is a+c, where c is known.

The distance from point D to P is a+d, where d is known.

Note that b, c, and/or d may a negative value.

What is the distance from P to the plane containing ABCD?

(What is a--the length of AP?)