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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: 12
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche} \qquad A \qquad [m^{2}] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\
\\ b = \frac{A}{a}\\ \textbf{Gegeben:} \\ A=-1m^{2} \qquad a=3\frac{1}{5}m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{A}{a} \\
A=-1m^{2}\\
a=3\frac{1}{5}m\\
b = \frac{-1m^{2}}{3\frac{1}{5}m}\\\\b=-\frac{5}{16}m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline -1 m^2 \\ \hline -100 dm^2 \\ \hline -10^{4} cm^2 \\ \hline -10^{6} mm^2 \\ \hline -\frac{1}{100} a \\ \hline -0,0001 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3\frac{1}{5} m \\ \hline 32 dm \\ \hline 320 cm \\ \hline 3,2\cdot 10^{3} mm \\ \hline 3,2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline -\frac{5}{16} m \\ \hline -3\frac{1}{8} dm \\ \hline -31\frac{1}{4} cm \\ \hline -312\frac{1}{2} mm \\ \hline -3,13\cdot 10^{5} \mu m \\ \hline \end{array} \end{array}$