Olympiad Geometry · Superchallenge problem

A triangle has base $12$ and height $6$. A square is placed inside it with one side on the base and its top two corners on the other two sides. A second square is placed the same way in the small triangle above the first square (its bottom side on the top of the first square), a third square in the triangle above that, and so on forever. Find the total area of all the squares.