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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: 13
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche} \qquad A \qquad [m^{2}] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\
\\ b = \frac{A}{a}\\ \textbf{Gegeben:} \\ A=\frac{4}{7}m^{2} \qquad a=\frac{1}{2}m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{A}{a} \\
A=\frac{4}{7}m^{2}\\
a=\frac{1}{2}m\\
b = \frac{\frac{4}{7}m^{2}}{\frac{1}{2}m}\\\\b=1\frac{1}{7}m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline \frac{4}{7} m^2 \\ \hline 57\frac{1}{7} dm^2 \\ \hline 5714\frac{2}{7} cm^2 \\ \hline 571428\frac{4}{7} mm^2 \\ \hline 0,00571 a \\ \hline 5,71\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{1}{2} m \\ \hline 5 dm \\ \hline 50 cm \\ \hline 500 mm \\ \hline 5\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{7} m \\ \hline 11\frac{3}{7} dm \\ \hline 114\frac{2}{7} cm \\ \hline 1142\frac{6}{7} mm \\ \hline 1142857\frac{1}{7} \mu m \\ \hline \end{array} \end{array}$