A flat quadrilateral ABCD is divided into a triangle CDE and a trapezoid abce by the line CE, with the height of AF = 6cm. It is known that the area of trapezoid abce is 9cm larger than that of triangle CDE. How many cm is the length of trapezoid AE?

A flat quadrilateral ABCD is divided into a triangle CDE and a trapezoid abce by the line CE, with the height of AF = 6cm. It is known that the area of trapezoid abce is 9cm larger than that of triangle CDE. How many cm is the length of trapezoid AE?

Area of trapezoidal abce = 1 / 2 * (BC + AE) * ah = 1 / 2 * (BC + AE) * 6 = 3 (BC + AE)
Triangle CDE = 1 / 2 * de * ah = 1 / 2 * de * 6 = 3DE
The area of trapezoidal abce is 9 square centimeters larger than that of triangular CDE
3(BC+AE) - 3DE = 9
BC+AE- DE = 3
Also: BC = ad, de = ad-ae
∴AD+AE-(AD-AE) =3
2AE = 3
AE = 1.5