Geometrie-Viereck-Rechteck

$A = a\cdot b$
1 2 3 4 5 6 7 8 9 10 11 12
$a = \frac{A}{b}$
1 2 3 4 5
$b = \frac{A}{a}$
1 2 3 4 5 6 7 8 9 10 11 12 13
$U = 2\cdot a + 2\cdot b$
1 2 3 4 5 6 7 8 9 10 11 12 13
$a = \frac{U - 2\cdot b}{ 2}$
1 2 3 4 5 6 7 8 9 10 11
$b = \frac{U - 2\cdot a}{ 2}$
1 2 3 4 5 6 7 8 9 10 11 12
$d = \sqrt{a^{2} +b^{2} }$
1 2 3 4 5 6 7 8 9 10 11 12
$b = \sqrt{d^{2} -a^{2} }$
1 2 3 4 5 6 7 8 9 10
$a = \sqrt{d^{2} -b^{2} }$
1 2 3 4 5 6 7 8 9 10
Beispiel Nr: 10
$\begin{array}{l} \text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\ \text{Länge} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Diagonale} \qquad d \qquad [m] \\ \\ d = \sqrt{a^{2} +b^{2} }\\ \textbf{Gegeben:} \\ b=\frac{1}{50}m \qquad a=\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ d = \sqrt{a^{2} +b^{2} } \\ b=\frac{1}{50}m\\ a=\frac{2}{5}m\\ d = \sqrt{(\frac{2}{5}m)^{2} +(\frac{1}{50}m)^{2} }\\\\d=0,4m \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline \frac{1}{50} m \\ \hline \frac{1}{5} dm \\ \hline 2 cm \\ \hline 20 mm \\ \hline 2\cdot 10^{4} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{2}{5} m \\ \hline 4 dm \\ \hline 40 cm \\ \hline 400 mm \\ \hline 4\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline d=\\ \hline 0,4 m \\ \hline 4 dm \\ \hline 40 cm \\ \hline 400 mm \\ \hline 4\cdot 10^{5} \mu m \\ \hline \end{array} \end{array}$