The shape of a molecule or ion is determined by its molecular geometry, which is based on the arrangement of its atoms and lone pairs around the central atom. In the case of the cuprammonium ion (Cu(NH3)4^2+), the central atom is copper (Cu).

To determine the shape of the cuprammonium ion, we need to consider the number of regions of electron density around the central atom. These regions include both bonded atoms and lone pairs. In this case, there are four regions of electron density around the central copper atom.

Using the VSEPR (Valence Shell Electron Pair Repulsion) theory, we can predict the shape of the cuprammonium ion. The VSEPR theory states that electron pairs repel each other and will arrange themselves in a way that minimizes this repulsion.

- TETRAHEDRAL GEOMETRY:
With four regions of electron density, the ideal molecular geometry for the cuprammonium ion would be tetrahedral. In a tetrahedral geometry, the four regions of electron density are arranged in a three-dimensional shape, resembling a pyramid with a triangular base. Each of the four ammonia (NH3) ligands surrounding the central copper atom would be positioned at the four corners of the tetrahedron.

- SQUARE PLANAR GEOMETRY:
However, the cuprammonium ion is an exception to the VSEPR theory because of the presence of a d-orbital in the central copper atom. The d-orbital can participate in bonding and can influence the shape of the molecule. In this case, the copper atom uses its d-orbital to form a coordinate bond with one of the nitrogen atoms in the ammonia ligands, resulting in a square planar geometry.

In a square planar geometry, the four ammonia ligands are arranged in a flat plane around the central copper atom, with bond angles of approximately 90 degrees. This geometry is characterized by the presence of a square in the plane formed by the ligands.

Therefore, the correct answer is option D: Square planar.