Aufgabengruppe I

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

$\overline{AF}={\displaystyle \frac{72c{m}^2}{8cm}}\Rightarrow \underline{\overline{AF}=9cm}$

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

$\overline{CF}=9\cdot \tan 25°\Rightarrow \overline{CF}=9\cdot \mathrm{0,4663}$

$\underline{\overline{CF}=\mathrm{4,1967}cm}$

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

$\overline{BF}={\displaystyle \frac{{\left(\overline{CF}\right)}^2}{\overline{AF}}}\Rightarrow \overline{BF}={\displaystyle \frac{{\left(\mathrm{4,1967}cm\right)}^2}{9cm}}$

$\underline{\overline{BF}=\mathrm{1,9569}cm}$

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

$A_{\text{ABCD}}={\displaystyle \frac{1}{2}}\cdot (9cm+\mathrm{1,9569}cm)\cdot \mathrm{4,1967}cm$

$A_{\text{ABCD}}=23c{m}^2$