11.11. What is the maximum area of the projection of a rectangular parallelepiped with edges $a, b$, and $c$ onto a plane?
11.11. The area of the projection of a parallelepiped is at least twice the area of the projection of one of the triangles with vertices at the ends of three edges of the parallelepiped emanating from one point; for example, if the projection of the parallelepiped is a hexagon, then as such a vertex, one should take the vertex whose projection lies inside the pentagon. For a rectangular parallelepiped, all such triangles are equal. Therefore, the area of the projection of the parallelepiped will be the largest when one of these triangles is parallel to the projection plane. It will be equal to $\sqrt{a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2}}$ (see figure $\mathbf{1 . 2 2 )}$.