a) Vì B'C' // BC theo định lí Ta-lét ta có:

$\frac{B'C'}{BC}$ = $\frac{AB'}{AB}$

Vì B'D' // BD theo định lí Ta-lét ta có:

$\frac{AD'}{AD}$ = $\frac{AB'}{AB}$

Suy ra: $\frac{AD'}{AD}$ = $\frac{B'C'}{BC}$.

b) Theo kết quả câu a: $\frac{B'C'}{BC}$ = $\frac{AD'}{AD}$ $\Leftrightarrow $ $\frac{B'C'}{BC}$ = $\frac{1}{4}$ 

Ta có: S$\Delta $ABC = $\frac{1}{2}$AD.BC 

           S$\Delta $AB'C' = $\frac{1}{2}$AD'.B'C'

$\Leftrightarrow $ $\frac{ S\Delta ABC }{S\Delta AB'C'}$ = $\frac{\frac{1}{2}AD.BC }{\frac{1}{2}AD'.B'C'}$

$\Leftrightarrow $ $\frac{73,2}{S\Delta AB'C'}$ = $\frac{AD.BC}{AD'.B'C'}$ = $\frac{AD}{AD'}$. $\frac{BC}{B'C'}$ = 4.4 = 16

Suy ra S$\Delta $AB'C' = $\frac{73,2}{16}$ = 4,575 $cm^{2}$