6.
P = a · b
a)
[tex]a = \sqrt{3} \ cm\\b = \sqrt{27} \ cm[/tex]
[tex]P = \sqrt{3}\cdot\sqrt{27} = \sqrt{3\cdot27} = \sqrt{81} \ =\boxed{ 9 \ cm^{2}}[/tex]
b)
[tex]a = 2\sqrt{6} \ cm\\b = 6\sqrt{2} \ cm\\\\P = 2\sqrt{6}\cdot6\sqrt{2} = 12\sqrt{6\cdot2} = 12\sqrt{12} = 12\cdot\sqrt{4\cdot3} = 12\cdot\sqrt{4}\cdot\sqrt{3} = 12\cdot2\sqrt{3} = \\\\=\boxed{24\sqrt{3} \ cm^{2}}[/tex]
c)
[tex]a = 3\sqrt{15} \ cm\\b = 2\sqrt{10} \ cm\\\\P = 3\sqrt{15}\cdot2\sqrt{10} = 6\sqrt{15\cdot10} = 6\sqrt{150} = 6\sqrt{25\cdot6}=6\cdot\sqrt{25}\cdot\sqrt{6} = 6\cdot5\sqrt{6} =\\\\=\boxed{30\sqrt{6} \ cm^{2}}[/tex]
