Der Umfang der graugefärbten Fläche berechnet sich mit der Formel

$U=a+b+cU\; =\; a\; +\; b\; +\; c$,

wobei $aa$, $bb$ und $cc$ die Seiten dieses Dreiecks sind.

$cc$ lässt sich sehr schnell berechnen (siehe Skizze):

$c=4\cdot 8\text{cm}=32\text{cm}c=\; 4\; \backslash cdot\; 8\; \backslash ;\backslash text\{cm\}=\; 32\; \backslash ;\backslash text\{cm\}$

${\left(\frac{a}{2}\right)}^2=(8\text{cm}{)}^2+(6\text{cm}{)}^2\backslash left(\backslash frac\{a\}2\backslash right)^2=\; (8\; \backslash ;\backslash text\{cm\})^2+(6\; \backslash ;\backslash text\{cm\})^2$

$\left(\frac{a}{2}\right)=\sqrt{(8\text{cm}{)}^2+(6\text{cm}{)}^2}\backslash left(\backslash frac\{a\}2\backslash right)=\; \backslash sqrt\{(8\; \backslash ;\backslash text\{cm\})^2+(6\; \backslash ;\backslash text\{cm\})^2\}$

$\left(\frac{a}{2}\right)=\sqrt{64{\text{cm}}^2+36{\text{cm}}^2}\backslash left(\backslash frac\{a\}2\backslash right)=\; \backslash sqrt\{64\; \backslash ;\backslash text\{cm\}^2+36\; \backslash ;\backslash text\{cm\}^2\}$

$\left(\frac{a}{2}\right)=\sqrt{100{\text{cm}}^2}\backslash left(\backslash frac\{a\}2\backslash right)=\; \backslash sqrt\{100\backslash ;\backslash text\{cm\}^2\}$

$\left(\frac{a}{2}\right)=10\text{cm}\backslash left(\backslash frac\{a\}2\backslash right)=\; 10\; \backslash ;\backslash text\{cm\}$

$\Rightarrow a=2\cdot 10\text{cm}=20\text{cm}\backslash Rightarrow\; a\; =\; 2\; \backslash cdot\; 10\; \backslash ;\; \backslash text\{cm\}\; =\; 20\backslash ,\backslash text\{cm\}$

$\Rightarrow b=20\text{cm}\backslash Rightarrow\; b\; =\; 20\backslash ,\backslash text\{cm\}$

$\Rightarrow U=a+b+c=20\text{cm}+20\text{cm}+32\text{cm}=72\text{cm}\backslash Rightarrow\; U\; =\; a\; +\; b\; +\; c=\; 20\backslash ,\backslash text\{cm\}\; +\; 20\backslash ,\backslash text\{cm\}\; +\; 32\backslash ,\backslash text\{cm\}=\; 72\backslash ,\backslash text\{cm\}$