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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: 04
$\begin{array}{l}
\text{Gegeben:}\\\text{Seite} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\
\\ A = \frac{a^{2} }{4}\cdot \sqrt{3}\\ \textbf{Gegeben:} \\ a=0,002m \qquad \\ \\ \textbf{Rechnung:} \\
A = \frac{a^{2} }{4}\cdot \sqrt{3} \\
a=0,002m\\
A = \frac{(0,002m)^{2} }{4}\cdot \sqrt{3}\\\\A=1,73\cdot 10^{-6}m^{2}
\\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 0,002 m \\ \hline \frac{1}{50} dm \\ \hline \frac{1}{5} cm \\ \hline 2 mm \\ \hline 2\cdot 10^{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 1,73\cdot 10^{-6} m^2 \\ \hline 0,000173 dm^2 \\ \hline 0,0173 cm^2 \\ \hline 1,73 mm^2 \\ \hline 1,73\cdot 10^{-8} a \\ \hline 1,73\cdot 10^{-10} ha \\ \hline \end{array} \end{array}$