A rectangle has both diagonals, and a flat line is drawn across it a quarter of the way down from the top. How many triangles can be counted?

By size: 2 tiny corner triangles above the flat line, 1 small triangle between the flat line and the centre, 4 quarter triangles meeting at the centre, 2 triangles with the flat line as their top side, and 4 halves of the rectangle: $2+1+4+2+4=13$.