The area of triangle AEF is equal to the area of quadrangle AEF minus the area of triangle ECF. Because the area of rectangular ABCD is equal to the sum of the areas of triangle ABE, ADF and quadrilateral AECF, and they are equal, the area of quadrilateral AECF is equal to one third of the rectangle. Because the length and width of rectangular ABCD are 9 cm and 6 cm respectively, it is easy to find its area, so the key to solve the problem is to find the area of triangular ECF. According to the triangle area formula, if we know the length of AB, we can find BE, EC and FC. In this way, the problem is solved.

Solution: Rectangular ABCD: 9× 6 = 54 (cm? ) quadrilateral aecf: 54 ÷ 3 = 18 (cm? ) EC:9- 18×2÷6=3 (cm)

FC:6- 18×2÷9 = 2(cm)AEF: 18-3×2÷2 = 15(cm？ )