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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: 09
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche} \qquad A \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Seite} \qquad a \qquad [m] \\
\\ a = \sqrt{\frac{A\cdot 4}{\sqrt{3}}}\\ \textbf{Gegeben:} \\ A=1\frac{1}{5}m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
a = \sqrt{\frac{A\cdot 4}{\sqrt{3}}} \\
A=1\frac{1}{5}m^{2}\\
a = \sqrt{\frac{1\frac{1}{5}m^{2}\cdot 4}{\sqrt{3}}}\\\\a=1,66m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline 1\frac{1}{5} m^2 \\ \hline 120 dm^2 \\ \hline 1,2\cdot 10^{4} cm^2 \\ \hline 1,2\cdot 10^{6} mm^2 \\ \hline 0,012 a \\ \hline 0,00012 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1,66 m \\ \hline 16,6 dm \\ \hline 166 cm \\ \hline 1,66\cdot 10^{3} mm \\ \hline 1,66\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$