Rysunek pomocniczy:

Z tw. Pitagorasa otrzymujemy:

$x^2+h^2={\left(3\sqrt{2}\right)}^2$  

$x^2+h^2=18$  

$h^2=18-x^2$      

 

Z tw. Pitagorasa otrzymujemy:

${\left(6-x\right)}^2+h^2={\sqrt{6}}^2$  

$36-12x+x^2+18-x^2=6$  

$48-12x=0\mid +12x$  

$48=12x\mid :12$  

$x=4$  

 

$h^2=18-4^2$  

$h^2=18-16$  

$h^2=2$  

$h=\sqrt{2}$  

 

$\sin \alpha =\frac{h}{3\sqrt{2}}$  

$\sin \alpha =\frac{\sqrt{2}}{3\sqrt{2}}$  

$\sin \alpha =\frac{1}{3}$  

 

$\text{Obw}=6+3\sqrt{2}+6-x+h$  

$\text{Obw}=6+3\sqrt{2}+6-4+\sqrt{2}$  

$\text{Obw}=8+4\sqrt{2}$