A rectangle stands on the base of a triangle with its top corners on the sides, and both diagonals of the rectangle are drawn. How many quadrilaterals are there?

Below the rectangle's top edge, with that edge as a side: the rectangle, the whole lower trapezium, the rectangle with one end triangle (2), and an end triangle with the half of the rectangle beside it (2), 6. An end triangle with the quarter beside it, 2. Including the top triangle: with the top quarter (1), with a half of the rectangle (2), with the rectangle and one end triangle (2), and with a half and the end triangle beyond it (2), 7. Total $6+2+7=15$.