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$ A = \frac{a^{2} }{4}\cdot \sqrt{3} $
$ a = \sqrt{\frac{A\cdot 4}{\sqrt{3}}} $
$ h = \frac{a}{2}\cdot \sqrt{3} $
$ a = \frac{h\cdot 2}{\sqrt{3}} $
Geometrie-Dreieck-Gleichseitiges Dreieck
$A = \frac{a^{2} }{4}\cdot \sqrt{3}$
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$a = \sqrt{\frac{A\cdot 4}{\sqrt{3}}}$
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$h = \frac{a}{2}\cdot \sqrt{3}$
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$a = \frac{h\cdot 2}{\sqrt{3}}$
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Beispiel Nr: 01
$\begin{array}{l}
\text{Gegeben:}\\\text{Höhe} \qquad h \qquad [m] \\
\\ \text{Gesucht:} \\\text{Seite} \qquad a \qquad [m] \\
\\ a = \frac{h\cdot 2}{\sqrt{3}}\\ \textbf{Gegeben:} \\ h=9m \qquad \\ \\ \textbf{Rechnung:} \\
a = \frac{h\cdot 2}{\sqrt{3}} \\
h=9m\\
a = \frac{9m\cdot 2}{\sqrt{3}}\\\\a=10,4m
\\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 9 m \\ \hline 90 dm \\ \hline 900 cm \\ \hline 9\cdot 10^{3} mm \\ \hline 9\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 10,4 m \\ \hline 104 dm \\ \hline 1,04\cdot 10^{3} cm \\ \hline 1,04\cdot 10^{4} mm \\ \hline 1,04\cdot 10^{7} \mu m \\ \hline \end{array} \end{array}$