${\left|EC\right|}^2=4^2+8^2$

${\left|EC\right|}^2=16+64$

${\left|EC\right|}^2=80$     $/\sqrt{}$

$\left|EC\right|=\sqrt{80}$

$\left|EC\right|=\sqrt{16\cdot 5}$

$\left|EC\right|=4\sqrt{5}cm$

 

|CF|=|EC|        (takie same przyprostokątne trójkątów prostokątne ECD i FBC)

 

${\left|EF\right|}^2=4^2+4^2$

${\left|EF\right|}^2=16+16$

${\left|EF\right|}^2=32$             $/\sqrt{}$

$\left|EF\right|=\sqrt{32}$

$\left|EF\right|=\sqrt{16\cdot 2}=4\sqrt{2}cm$

 

$O_{EFC}=4\sqrt{2}cm+2\cdot 4\sqrt{5}cm=4\sqrt{2}m+8\sqrt{5}cm=\underline{\underline{4\left(\sqrt{2}+2\sqrt{5}\right)cm}}$

 

Obliczmy długość wysokości trójkąt EFG

$h^2+{\left(\frac{1}{2}\left|EF\right|\right)}^2={\left|CF\right|}^2$

$h^2+{\left(2\sqrt{2}\right)}^2={\left(4\sqrt{5}\right)}^2$

$h^2+4\cdot 2=16\cdot 5$

$h^2+8=80$

$h^2=80-8$

$h^2=72$     $/\sqrt{}$

$h=\sqrt{72}$

$h=\sqrt{36\cdot 2}$

$h=6\sqrt{2}cm$

$P=\frac{1}{2}\cdot \left|EF\right|\cdot h=\frac{1}{2}\cdot 4\sqrt{2}cm\cdot 6\sqrt{2}cm=2\sqrt{2}cm\cdot 6\sqrt{2}cm=12\cdot 2c{m}^2=\underline{\underline{24c{m}^2}}$