Pyramid Section (AR Modeling Challenge)

In this GeoGebra Augmented Reality Modeling challenge, the goal is to author 2 surface equations (with domain restrictions) to recreate what is seen in the screencast below. The blue surface consists of 4 congruent isosceles trapezoids. The pink surface is a square. Modeling Clues: 1) If the non-parallel edges of the 4 blue isosceles trapezoids were to extend upwards, they would all meet at (0,0,5). That is, these 4 isosceles trapezoids are part of a square pyramid whose apex lies at (0,0,5). 2) Suppose the height of this pyramid (described in (1)) = h. Suppose the distance from the center of the base of this pyramid to a vertex of this base = r. Here, in this screencast, we have . 3) The longer base of each isosceles trapezoid measures units.

Quick Demo