Explicație pas cu pas:
[tex]EF^{2} = DE^{2} + DF^{2} = {(3 \sqrt{2})}^{2} + {6}^{2} =18 + 36 = 54 \\ EF=3 \sqrt{6} \: cm[/tex]
[tex]DE^{2} = EG \times EF = > EG = \frac{18}{3 \sqrt{6} } = \sqrt{6} cm[/tex]
[tex]DF^{2} = GF \times EF = > GF = \frac{36}{3 \sqrt{6} } = 2 \sqrt{6} \: cm [/tex]
[tex]DG^{2} = EG \times GF = > DG = \sqrt{ \sqrt{6} \times 2 \sqrt{6}} = \sqrt{12} = 2 \sqrt{3} \: cm[/tex]
[tex]Aria(DEG) = \frac{DG \times EG}{2} = \frac{2 \sqrt{3} \times \sqrt{6}}{2} = 3 \sqrt{2} \: {cm}^{2} [/tex]
[tex]Aria(DFG) = \frac{DG \times GF}{2} = \frac{2 \sqrt{3} \times 2\sqrt{6} }{2} = 6 \sqrt{3} \: {cm}^{2} [/tex]
