When three $1 imes 1 imes 1$ cubes are joined together as in the diagram, the resulting prism is $3 imes 1 imes 1$. This prism has four rectangular faces that are $3 imes 1$ and two rectangular faces that are $1 imes 1$. Therefore, the surface area is $4 imes(3 imes 1)+2 imes(1 imes 1)=4 imes 3+2 imes 1=12+2=14$.