Geometrie-Viereck-Allgemeines 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: 05
$\text{Gegeben:}\\\text{Grundlinie c} \qquad c \qquad [m] \\ \text{Grundlinie} \qquad a \qquad [m] \\ \text{Fläche} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad h \qquad [m] \\ \\ h = \frac{2\cdot A}{a+c}\\ \textbf{Gegeben:} \\ c=4m \qquad a=4m \qquad A=46m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ h = \frac{2\cdot A}{a+c} \\ c=4m\\ a=4m\\ A=46m^{2}\\ h = \frac{2\cdot 46m^{2}}{4m+4m}\\\\h=11\frac{1}{2}m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 46 m^2 \\ \hline 4,6\cdot 10^{3} dm^2 \\ \hline 4,6\cdot 10^{5} cm^2 \\ \hline 4,6\cdot 10^{7} mm^2 \\ \hline \frac{23}{50} a \\ \hline 0,0046 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 11\frac{1}{2} m \\ \hline 115 dm \\ \hline 1,15\cdot 10^{3} cm \\ \hline 1,15\cdot 10^{4} mm \\ \hline 1,15\cdot 10^{7} \mu m \\ \hline \end{array}$