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: 06
$ \text{Gegeben:}\\\text{Grundlinie c} \qquad c \qquad [m] \\ \text{Grundlinie a} \qquad a \qquad [m] \\ \text{Höhe} \qquad h \qquad [m] \\ \\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\ \\ A = \frac{a+c}{ 2}\cdot h\\ \textbf{Gegeben:} \\ c=2\frac{2}{5}m \qquad a=3m \qquad h=5m \qquad \\ \\ \textbf{Rechnung:} \\ A = \frac{a+c}{ 2}\cdot h \\ c=2\frac{2}{5}m\\ a=3m\\ h=5m\\ A = \frac{3m+2\frac{2}{5}m}{ 2}\cdot 5m\\\\A=13\frac{1}{2}m^{2} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 2\frac{2}{5} m \\ \hline 24 dm \\ \hline 240 cm \\ \hline 2,4\cdot 10^{3} mm \\ \hline 2,4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \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 h=\\ \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 13\frac{1}{2} m^2 \\ \hline 1,35\cdot 10^{3} dm^2 \\ \hline 1,35\cdot 10^{5} cm^2 \\ \hline 1,35\cdot 10^{7} mm^2 \\ \hline 0,135 a \\ \hline 0,00135 ha \\ \hline \end{array}$