Geometrie-Stereometrie-Quader

$V = a\cdot b\cdot c$
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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
$\begin{array}{l} \text{Gegeben:}\\\text{Höhe} \qquad c \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Länge} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ O = 2\cdot (a\cdot b + a\cdot c + b\cdot c)\\ \textbf{Gegeben:} \\ c=5m \qquad b=2m \qquad a=8m \qquad \\ \\ \textbf{Rechnung:} \\ O = 2\cdot (a\cdot b + a\cdot c + b\cdot c) \\ c=5m\\ b=2m\\ a=8m\\ O = 2\cdot (8m\cdot 2m + 8m \cdot 5m + 2m\cdot 5m)\\\\O=132m^{2} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 132 m^2 \\ \hline 1,32\cdot 10^{4} dm^2 \\ \hline 1,32\cdot 10^{6} cm^2 \\ \hline 1,32\cdot 10^{8} mm^2 \\ \hline 1\frac{8}{25} a \\ \hline 0,0132 ha \\ \hline \end{array} \end{array}$