Geometrie-Viereck-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: 04
$\text{Gegeben:}\\\text{Grundlinie a} \qquad a \qquad [m] \\ \text{Höhe} \qquad h \qquad [m] \\ \text{Fläche} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Grundlinie c} \qquad c \qquad [m] \\ \\ c = \frac{2\cdot A}{ h} - a\\ \textbf{Gegeben:} \\ a=2m \qquad h=3m \qquad A=30m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ c = \frac{2\cdot A}{ h} - a \\ a=2m\\ h=3m\\ A=30m^{2}\\ c = \frac{2\cdot 30m^{2}}{ 3m} - 2m\\\\c=18m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 30 m^2 \\ \hline 3\cdot 10^{3} dm^2 \\ \hline 3\cdot 10^{5} cm^2 \\ \hline 3\cdot 10^{7} mm^2 \\ \hline \frac{3}{10} a \\ \hline 0,003 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 18 m \\ \hline 180 dm \\ \hline 1,8\cdot 10^{3} cm \\ \hline 1,8\cdot 10^{4} mm \\ \hline 1,8\cdot 10^{7} \mu m \\ \hline \end{array}$