Explicație pas cu pas:
[tex]\tan(30) =\frac{DG}{GF} \\ = > DG = \frac{ \sqrt{3} }{3} \times 6 \sqrt{2} = 2 \sqrt{6} [/tex]
[tex]DG^{2} = EG \times GF \\ EG = \frac{DG^{2}}{GF} = \frac{24}{6 \sqrt{2} } = 2 \sqrt{2} [/tex]
[tex]EF = EG + GF = 2 \sqrt{2} + 6 \sqrt{2} = 8 \sqrt{2} [/tex]
[tex]aria = \frac{DG \times EF}{2} = \frac{2 \sqrt{6} \times 8 \sqrt{2} }{2} = 16 \sqrt{3} \: cm^{2} [/tex]
[tex]DE = EF \times \sin(30) = 8 \sqrt{2} \times \frac{1}{2} = 4 \sqrt{2} [/tex]
[tex]DF = EF \times \cos(30) = \frac{8 \sqrt{2} \times \sqrt{3} }{2} = 4 \sqrt{6} [/tex]
[tex]perimetrul = DE + DF + EF = 4 \sqrt{2} + 4 \sqrt{6} +8\sqrt{2} = 12 \sqrt{2} + 4\sqrt{6} =4 \sqrt{2} (3 + \sqrt{3} ) \: cm[/tex]
