Both long diagonals are drawn across a rectangle made of two rows and four columns of equal squares. Find the total number of triangles.

Take the smallest triangle as 1 unit. Sizes found: 8 of 1 unit, 2 of 2 units, 8 of 4 units, 4 of 8 units (the quarters meeting at the centre), 4 of 9 units and 4 of 16 units (the halves of the rectangle). Total $8+2+8+4+4+4=30$.