A rectangle joins the midpoints of the sides of a rhombus, and both diagonals of the rhombus are drawn. How many triangles are there in all?

By size: the rectangle leaves a triangle at each corner of the rhombus, and each is halved by a diagonal, giving 8 smallest and 4 whole. The diagonals also cut the rhombus into 4 quarters and 4 halves. Total $8+4+4+4=20$.