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$ A = a\cdot b $
$ a = \frac{A}{b} $
$ b = \frac{A}{a} $
$ U = 2\cdot a + 2\cdot b $
$ a = \frac{U - 2\cdot b}{ 2} $
$ b = \frac{U - 2\cdot a}{ 2} $
$ d = \sqrt{a^{2} +b^{2} } $
$ b = \sqrt{d^{2} -a^{2} } $
$ a = \sqrt{d^{2} -b^{2} } $
Geometrie-Viereck-Rechteck
$A = a\cdot b$
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$a = \frac{A}{b}$
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$b = \frac{A}{a}$
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$U = 2\cdot a + 2\cdot b$
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$a = \frac{U - 2\cdot b}{ 2}$
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$b = \frac{U - 2\cdot a}{ 2}$
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$d = \sqrt{a^{2} +b^{2} }$
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$b = \sqrt{d^{2} -a^{2} }$
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$a = \sqrt{d^{2} -b^{2} }$
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Beispiel Nr: 02
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Fläche} \qquad A \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\
\\ a = \frac{A}{b}\\ \textbf{Gegeben:} \\ b=7m \qquad A=2m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
a = \frac{A}{b} \\
b=7m\\
A=2m^{2}\\
a = \frac{2m^{2}}{7m}\\\\a=\frac{2}{7}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 2 m^2 \\ \hline 200 dm^2 \\ \hline 2\cdot 10^{4} cm^2 \\ \hline 2\cdot 10^{6} mm^2 \\ \hline \frac{1}{50} a \\ \hline 0,0002 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{2}{7} m \\ \hline 2\frac{6}{7} dm \\ \hline 28\frac{4}{7} cm \\ \hline 285\frac{5}{7} mm \\ \hline 285714\frac{2}{7} \mu m \\ \hline \end{array} \end{array}$