Solution: If D is the vertical DM of BC extension line and M is the vertical foot (or △ADP rotates 90 degrees around D to make DA and DC coincide), then: ∠ DMC = 90 degrees.

So the quadrilateral PBMD is a rectangle (three right angles), so: ∠ PDM = 90 degrees = ∠ PDC+∠ CDM.

And: ∠ ADC = 90 degrees = ∠ ADP+∠ PDC: ∠ CDM = ∠ ADP.

Also: DP⊥AB Reason: ∠ APD = 90 degrees = ∠ DMC.

Ad = CD: △ DAP △ DCM: DP = DM quadrilateral area PBMD = quadrilateral area AD=CD = 36.

Because quadrilateral PBMD is a rectangle DP = DM, quadrilateral PBMD is a square.

That is, the square of PBMD is 36, so DP = √ 36 = 6.