Hugo sent us pictures of his solution. Well done, Hugo!

" I know that the area of a triangle is given by the forumula

${\displaystyle \frac{1}{2}\times \mathrm{base}\times \mathrm{height}.}$

The original triangle has base 1 and height 1, so as long as each triangle on the way also has base 1 and height 1 the area will stay the same".