• $V = a\cdot b\cdot c$
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$a = \frac{ V}{b\cdot c}$
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$b = \frac{ V}{a\cdot c}$
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$c = \frac{ V}{b\cdot a}$
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$O = 2\cdot (a\cdot b + a\cdot c + b\cdot c)$
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$a = \frac{O-2\cdot b\cdot c}{2\cdot (b+c)}$
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$b = \frac{O-2\cdot a\cdot c}{2\cdot (a+c)}$
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$c = \frac{O-2\cdot b\cdot a}{2\cdot (b+a)}$
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$d = \sqrt{a^{2} +b^{2} +c^{2} }$
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$a = \sqrt{d^{2} -b^{2} -c^{2} }$
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$b = \sqrt{d^{2} -a^{2} -c^{2} }$
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$c = \sqrt{d^{2} -b^{2} -a^{2} }$
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Beispiel Nr: 01
$\text{Gegeben:}\\\text{Länge} \qquad a \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad c \qquad [m] \\ \\ c = \frac{O-2\cdot b\cdot a}{2\cdot (b+a)}\\ \textbf{Gegeben:} \\ a=7m \qquad b=1m \qquad O=8m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ c = \frac{O-2\cdot b\cdot a}{2\cdot (b+a)} \\ a=7m\\ b=1m\\ O=8m^{2}\\ c = \frac{8m^{2}-2\cdot 1m\cdot 7m}{2\cdot (1m+7m)}\\\\c=-\frac{3}{8}m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 8 m^2 \\ \hline 800 dm^2 \\ \hline 8\cdot 10^{4} cm^2 \\ \hline 8\cdot 10^{6} mm^2 \\ \hline \frac{2}{25} a \\ \hline 0,0008 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline -\frac{3}{8} m \\ \hline -3\frac{3}{4} dm \\ \hline -37\frac{1}{2} cm \\ \hline -375 mm \\ \hline -3,75\cdot 10^{5} \mu m \\ \hline \end{array}$