• $V = a\cdot b\cdot c$
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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: 02
$\text{Gegeben:}\\\text{Höhe} \qquad c \qquad [m] \\ \text{Länge} \qquad a \qquad [m] \\ \text{Raumdiagonale} \qquad d \qquad [m] \\ \\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\ \\ b = \sqrt{d^{2} -a^{2} -c^{2} }\\ \textbf{Gegeben:} \\ c=9m \qquad a=6m \qquad d=10m \qquad \\ \\ \textbf{Rechnung:} \\ b = \sqrt{d^{2} -a^{2} -c^{2} } \\ c=9m\\ a=6m\\ d=10m\\ b = \sqrt{(10m)^{2} -(6m)^{2} -(9m)^{2} }\\\\b=NaNm \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 9 m \\ \hline 90 dm \\ \hline 900 cm \\ \hline 9\cdot 10^{3} mm \\ \hline 9\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline d=\\ \hline 10 m \\ \hline 100 dm \\ \hline 10^{3} cm \\ \hline 10^{4} mm \\ \hline 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline NaN m \\ \hline NaN dm \\ \hline NaN cm \\ \hline NaN mm \\ \hline NaN \mu m \\ \hline \end{array}$