A rectangle is divided into two rows and three columns, and both of its long diagonals are drawn. How many triangles are there?

By size: 4 halves of the rectangle, 4 quarters meeting at the centre, 4 between a diagonal and the middle flat line, 4 that span two columns, 4 in the corner cells, and 6 small ones around the centre in the middle column. Total $4+4+4+4+4+6=26$.