Triangle Count!

Considering the rectangle apex angle as the center of the figure, we have four groups of four triangles with the hypotenuse as the each side one of four squares formed by each group. Here are 16 triangles.

Considering the hypotenuse as the two diagonals of the four squares, we have two groups of four triangles in each of the diagonal. Here we have 16 triangles.

What makes total: $32$ .

Take the smallest triangle. There are 4 of that alone plus 4 triangles constructed by combining two small adjacent triangles. So we make 8 triangles only for the smallest ones. We can take the smallest triangle with the next layer and have a bit larger triangle. We can make the same thing as a bove and have another 8 triangles. There are total 4 layers so 4*8=32 triangles

Start from 1 single triangle and count toward the edge.

That’s 4 and you could repeat it for each edge. That’s 16.

Again, start from center from 2 triangles and count toward the corner.

That’s 4 and you could repeat it for each corner. That’s 16 more hence a total of 32.

Just count :D