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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: 05
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche} \qquad A \qquad [m^{2}] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\
\\ b = \frac{A}{a}\\ \textbf{Gegeben:} \\ A=9m^{2} \qquad a=8m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{A}{a} \\
A=9m^{2}\\
a=8m\\
b = \frac{9m^{2}}{8m}\\\\b=1\frac{1}{8}m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline 9 m^2 \\ \hline 900 dm^2 \\ \hline 9\cdot 10^{4} cm^2 \\ \hline 9\cdot 10^{6} mm^2 \\ \hline \frac{9}{100} a \\ \hline 0,0009 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{8} m \\ \hline 11\frac{1}{4} dm \\ \hline 112\frac{1}{2} cm \\ \hline 1,13\cdot 10^{3} mm \\ \hline 1,13\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$