Vì \(\left\{{}\begin{matrix}DF\perp AB\\AC\perp AB\end{matrix}\right.\)\(\Rightarrow\)DF // AC

\(\Rightarrow\dfrac{DF}{AC}=\dfrac{BD}{AB}\)(định lý Ta-lét) \(\Rightarrow\dfrac{DF}{AE+EC}=\dfrac{BD}{BD+DA}\Rightarrow\dfrac{DF}{DF+25}=\dfrac{20}{20+DA}\)(ADFE là hình chữ nhật(có 3 góc vuông))

\(\Rightarrow DF\left(20+DA\right)=20\left(DF+25\right)\Rightarrow20.DF+DF.DA=20.DF=500\Rightarrow DF.DA=500\)

mà DF.DA = \(S_{ADFE}\)\(\Rightarrow S_{ADFE}=500\left(cm^2\right)\)

Vậy\(S_{ADFE}=500cm^2\)