Given a quadrangular pyramid with a square base of side length 4, and lateral edges of lengths $4, 4, 2\sqrt{2}, 2\sqrt{2}$ respectively, find the height of the quadrangular pyramid.
Given a quadrangular pyramid with a square base of side length 4, and lateral edges of lengths $4, 4, 2\sqrt{2}, 2\sqrt{2}$ respectively, find the height of the quadrangular pyramid.