One of the five faces of the triangular prism shown here will be used as the base of a new pyramid. The numbers of exterior faces, vertices, and edges of the resulting shape (the fusion of the prism and pyramid) are added. What is the maximum value of this sum?
Thank You :P
The prism by itself:
5 faces 6 vertices 6 edges if you build off of one of the rectangular sides, you add
3 faces 1 vertice 4 edges if you build off of triangular side
2 faces 1 vertice 3 edges (note ONE face is covered in the original prism)
5 + 6 + 6 + 3 + 1 + 4 = 25