Surface Area and Volume · Superchallenge problem

Two identical triangular prisms are each $5$ cm long, and each end is a right triangle with legs of $6$ cm and $8$ cm and a longest side of $10$ cm. The two prisms are glued together so that one whole rectangular face of one prism exactly covers the matching face of the other. What is the smallest possible surface area of the new solid, in square centimeters?