For the two prisms to be congruent, what must the area of the base be, given that the triangular bases are congruent?

That two prisms are congruent means that they have the same measures of bases, height, faces and angles. This is they are the same figure, just the may be in different positions but you could superpose the two prisms 100%.

So, the area of the bases of the two congruent prisms are equal.