The sum of the lengths of the \(12\) edges of a cuboid is \(\quantity{x}{cm}\). The distance from one corner of the cuboid to the furthest corner is \(\quantity{y}{cm}\). What in \(\mathrm{cm^2}\) is the total surface area of the cuboid?

(A) \(\quad \dfrac{x^2-2y^2}{2} \qquad\) (B) \(\quad x^2+y^2 \qquad\) (C) \(\quad \dfrac{x^2-4y^2}{4} \qquad\) (D) \(\quad \dfrac{xy}{6} \qquad\) (E) \(\quad \dfrac{x^2-16y^2}{16}\)