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 $ A = \frac{a+c}{ 2}\cdot h $
                                      
                                          $ a = \frac{2\cdot A}{ h} - c $
                                      
                                          $ c = \frac{2\cdot A}{ h} - a $
                                      
                                          $ h = \frac{2\cdot A}{a+c} $
Geometrie-Viereck-Gleichschenkliges Trapez
 $A = \frac{a+c}{ 2}\cdot h$ 
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 $a = \frac{2\cdot A}{ h} - c$ 
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 $c = \frac{2\cdot A}{ h} - a$ 
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 $h = \frac{2\cdot A}{a+c}$ 
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                Beispiel Nr: 02
            
        
           $\begin{array}{l} 
      \text{Gegeben:}\\\text{Grundlinie c} \qquad c \qquad [m] \\
      \text{Grundlinie} \qquad a \qquad [m] \\
      \text{Fläche} \qquad A \qquad [m^{2}] \\
      \\ \text{Gesucht:} \\\text{Höhe} \qquad h \qquad [m] \\
     \\ h = \frac{2\cdot A}{a+c}\\ \textbf{Gegeben:} \\ c=4m \qquad a=5m \qquad A=20m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
      h = \frac{2\cdot A}{a+c} \\
      c=4m\\
      a=5m\\
      A=20m^{2}\\
      h = \frac{2\cdot 20m^{2}}{5m+4m}\\\\h=4\frac{4}{9}m
    \\\\\\ \small \begin{array}{|l|} \hline c=\\  \hline 4 m  \\  \hline 40 dm  \\  \hline 400 cm  \\  \hline 4\cdot 10^{3} mm  \\  \hline 4\cdot 10^{6} \mu m  \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\  \hline 5 m  \\  \hline 50 dm  \\  \hline 500 cm  \\  \hline 5\cdot 10^{3} mm  \\  \hline 5\cdot 10^{6} \mu m  \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\  \hline 20 m^2  \\  \hline 2\cdot 10^{3} dm^2  \\  \hline 2\cdot 10^{5} cm^2  \\  \hline 2\cdot 10^{7} mm^2  \\  \hline \frac{1}{5} a  \\  \hline 0,002 ha  \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\  \hline 4\frac{4}{9} m  \\  \hline 44\frac{4}{9} dm  \\  \hline 444\frac{4}{9} cm  \\  \hline 4444\frac{4}{9} mm  \\  \hline 4444444\frac{4}{9} \mu m  \\ \hline \end{array}  \end{array}$