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G
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$ V = G\cdot h $
$ G = \frac{V}{h} $
$ h = \frac{V}{G} $
$ O = 2\cdot G +M $
$ G = \frac{O-M}{2} $
$ M = O- 2\cdot G $
Geometrie-Stereometrie-Prisma
$V = G\cdot h$
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$G = \frac{V}{h}$
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$h = \frac{V}{G}$
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2
$O = 2\cdot G +M $
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$G = \frac{O-M}{2}$
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$M = O- 2\cdot G $
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Beispiel Nr: 02
$\begin{array}{l}
\text{Gegeben:}\\\text{Oberfläche} \qquad O \qquad [m^{2}] \\
\\\text{Mantelfläche} \qquad M \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Grundfläche} \qquad G \qquad [m^{2}] \\
\\ G = \frac{O-M}{2}\\ \textbf{Gegeben:} \\ O=540m^{2} \qquad M=30m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
G = \frac{O-M}{2} \\
M=30m^{2}\\
O=540m^{2}\\
G = \frac{540m^{2}-30m^{2}}{2}\\\
G=255m^{2}
\\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 540 m^2 \\ \hline 5,4\cdot 10^{4} dm^2 \\ \hline 5,4\cdot 10^{6} cm^2 \\ \hline 5,4\cdot 10^{8} mm^2 \\ \hline 5\frac{2}{5} a \\ \hline 0,054 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline M=\\ \hline 30 m^2 \\ \hline 3\cdot 10^{3} dm^2 \\ \hline 3\cdot 10^{5} cm^2 \\ \hline 3\cdot 10^{7} mm^2 \\ \hline \frac{3}{10} a \\ \hline 0,003 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 255 m^2 \\ \hline 2,55\cdot 10^{4} dm^2 \\ \hline 2,55\cdot 10^{6} cm^2 \\ \hline 2,55\cdot 10^{8} mm^2 \\ \hline 2\frac{11}{20} a \\ \hline 0,0255 ha \\ \hline \end{array} \end{array}$