Let $$ABCD$$ be a trapezium in which $$AB \parallel CD$$ and $$AB = 3CD$$. Let $$E$$ be the midpoint of the diagonal $$BD$$. If $$[ABCD] = n \times [CDE]$$, what is the value of $$n$$? (Here $$[\Gamma]$$ denotes the area of the geometrical figure $$\Gamma$$.)

Take $$CD = 1$$, $$AB = 3$$ and let $$h$$ be the distance between the parallel sides, so $$[ABCD] = \frac{1}{2}(3+1)h = 2h$$. Since $$E$$ is the midpoint of $$BD$$ and $$B$$ is at height $$h$$ while $$D$$ lies on line $$CD$$, the point $$E$$ is at height $$\frac{h}{2}$$ above $$CD$$. Hence $$[CDE] = \frac{1}{2} \times 1 \times \frac{h}{2} = \frac{h}{4}$$, and $$n = \frac{2h}{h/4} = 8$$.