Sally sent us her solution. She spotted
some interesting patterns: good work!
When I drew the squares, I knew the first one had side length 1,
then the third one had side length 2, the fifth had side length
4, and the seventh had side length 8 (they kept doubling). I drew
the picture on squared paper, and when I counted the squares,
each square (all of them, not just the odd ones) had area twice
as big as the one before. So the first one had area 1, then the
next one had area 2, then 4, then 8, then 16, then 32, then 64.
The area of the triangles is the area of the biggest one take
away the area of the next one down, so that's 64-32=32.