$A={\displaystyle \frac{1}{2}}\cdot e\cdot fA\; =\; \backslash dfrac\{1\}\{2\}\backslash cdot\; e\; \backslash cdot\; f$

Das ist die Flächenformel einer Raute.

Um $ee$ zu berechnen, musst du die Formel umstellen.

Jetzt kannst du $A=16{\text{cm}}^{2}A\; =\; 16\; \backslash ,\backslash text\{cm\}^2$ und $f=4\text{cm}f\; =\; 4\backslash ,\backslash text\{cm\}$ einsetzen.

$e={\displaystyle \frac{2\cdot A}{f}}={\displaystyle \frac{2\cdot 16{\text{cm}}^2}{4\text{cm}}}={\displaystyle \frac{32}{4}}\cdot {\displaystyle \frac{{\text{cm}}^2}{\text{cm}}}=8\text{cm}e\backslash \; =\backslash \; \backslash dfrac\{2\backslash cdot\; A\}\{f\}\backslash \; =\backslash \; \backslash dfrac\{2\backslash cdot\; 16\backslash ,\backslash text\{cm\}^2\}\{4\backslash ,\backslash text\{cm\}\}\backslash \; =\backslash \; \backslash dfrac\{32\}\{4\}\backslash cdot\; \backslash dfrac\{\backslash text\{cm\}^2\}\{\backslash text\{cm\}\}\backslash \; =\backslash \; 8\backslash ,\backslash text\{cm\}$

Antwort: Die Diagonale $ee$ hat also die Länge $8\text{cm}8\backslash ,\backslash text\{cm\}$.