How am I supposed to find the area of the shaded quadrilateral? In the diagram (which is not drawn to scale) the small triangles each have the area shown. Find the area of the shaded quadrilateral.



It can be deduced that the area $[FED] = 7\cdot 4/14=2$. 
Furthermore, examine the ratios below,
$$\frac{[FDC]}{[BDC]}=\frac{9}{18}=\frac{\frac{a}{a+b} \frac{d}{c+d}[ABC]  }{ \frac{b}{a+b}[ABC]}  =\frac ab  \frac{1}{\frac cd +1} \tag{1}$$
$$\frac{[FDB]}{[FCB]}=\frac{6}{21}=\frac{\frac{c}{c+d} \frac{b}{a+b} [ABC]  }{ \frac{d}{c+d} [ABC]}  =\frac cd  \frac{1}{\frac ab +1} \tag{2}$$
From (1) and (2), 
$$ \frac cd = \frac 12$$
Then, the area of the quadrilateral is
$$[AFED]= 2+ [AFD] = 2+\frac 12\cdot 9 = \frac {13}{2}$$
