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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: 11
$\begin{array}{l}
\text{Gegeben:}\\\text{Seite} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\
\\ A = \frac{a^{2} }{4}\cdot \sqrt{3}\\ \textbf{Gegeben:} \\ a=\frac{3}{5}m \qquad \\ \\ \textbf{Rechnung:} \\
A = \frac{a^{2} }{4}\cdot \sqrt{3} \\
a=\frac{3}{5}m\\
A = \frac{(\frac{3}{5}m)^{2} }{4}\cdot \sqrt{3}\\\\A=0,156m^{2}
\\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline \frac{3}{5} m \\ \hline 6 dm \\ \hline 60 cm \\ \hline 600 mm \\ \hline 6\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 0,156 m^2 \\ \hline 15,6 dm^2 \\ \hline 1,56\cdot 10^{3} cm^2 \\ \hline 1,56\cdot 10^{5} mm^2 \\ \hline 0,00156 a \\ \hline 1,56\cdot 10^{-5} ha \\ \hline \end{array} \end{array}$