zu a.) $\ A_{ADEF} = \overline{AD}\cdot\overline{AF}\ \Rightarrow\ 72\ cm^2 \ =\ 8\ cm\cdot\overline {AF}$

$\hspace{10mm}\overline{AF}\ =\ \dfrac{72\ cm^2 }{8\ cm}\ \Rightarrow\ \underline{\overline{AF}\ =\ 9\ cm}$

$\rule{10cm}{0.5mm}$

zu b.) $\tan\ \alpha=\ \frac{\overline{CF}}{\overline{AF}}\ \Rightarrow\ \overline{CF}\ =\ \overline{AF}\cdot\tan\ \alpha$

$\hspace{10mm}\overline{CF}\ =\ 9\cdot \tan\ 25° \Rightarrow\ \overline{CF}\ =\ 9\cdot0{,}4663$

$\hspace{10mm}\underline{\overline{CF}\ =\ 4{,}1967\ cm}$

$\rule{10cm}{0.5mm}$

zu c.) $\ \overline{AF}\cdot\overline{BF}\ =\ \left(\overline{CF}\right)^2\ \Rightarrow\ \$Höhensatz

$\hspace{10mm}\overline{BF}\ =\ \dfrac{\left(\overline{CF}\right)^2}{\overline{AF}}\ \Rightarrow\ \overline{BF}\ =\ \dfrac{\left(4{,}1967\ cm\right)^2}{9\ cm}$

$\hspace{10mm}\underline{\overline{BF}\ =\ 1{,}9569\ cm}$

$\rule{10cm}{0.5mm}$

zu d.)$\ A_\text{{ABCD}}\ =\ \dfrac{1}{2}\cdot\left(\overline{AF}+\overline{BF}\right)\cdot\overline{CF}$

$\hspace{8mm}\ A_\text{{ABCD}}\ =\ \dfrac{1}{2}\cdot\left(9\ cm+1{,}9569\ cm\right)\cdot4{,}1967\ cm$

$\hspace{8mm}\ \boxed{A_\text{{ABCD}}\ =\ 23\ cm^2}$