Odpowiedź:
a)
[tex]Obw = 2 * (\sqrt[3]{16} + \sqrt[3]{4}) = 2* (4^{\frac{2}{3}} + 4^{\frac{1}{3}})[/tex]
[tex]P = \sqrt[3]{16} * \sqrt[3]{4} = 4^{\frac{2}{3}} * 4^\frac{1}{3} = 4^{\frac{2}{3} + \frac{1}{3}} = 4^{\frac{3}{3}} = 4^{1} = 4[/tex]
b)
[tex]Obw = \sqrt{20} + \sqrt{5} + 5 = 2\sqrt{5} + \sqrt{5} + 5 = 3\sqrt{5} + 5[/tex]
[tex]P = \frac{a\ *\ h}{2} = \frac{\sqrt{20}\ *\ \sqrt{5}}{2} = \frac{\sqrt{100}}{2} = \frac{10}{2} = 5[/tex]
c)
[tex]Obw = \sqrt{2} + 5\sqrt{2} + \sqrt{32} + 4\sqrt{2} = \sqrt{2} + 5\sqrt{2} + 4\sqrt{2} + 4\sqrt{2} = 14\sqrt{2}[/tex]
[tex]P = \frac{(\sqrt{32} + \sqrt{2}) * 4\sqrt{2}}{2} = \frac{(4\sqrt{2} + \sqrt{2}) * 4\sqrt{2}}{2} = \frac{5\sqrt{2} * 4\sqrt{2}}{2} = \frac{40}{2} = 20[/tex]
d)
[tex]Obw = \sqrt{75} + \sqrt{75} + \sqrt{75} + \sqrt{75} = 4\sqrt{75} = 4 * 5\sqrt{3} = 20\sqrt{3}[/tex]
[tex]P = \frac{1}{2} * 6\sqrt{3} * 8\sqrt{3} * 1 = \frac{1}{2} * 144 = 72[/tex]
e)
[tex]Obw = 3\sqrt{5} + 5 + 6\sqrt{5} + 2\sqrt{10} = 5 + 9\sqrt{5} + 2\sqrt{10}[/tex]
[tex]P = \frac{(6\sqrt{5} + 3\sqrt{5})* 2\sqrt{5}}{2} = \frac{9\sqrt{5}*2\sqrt{5}}{2} = \frac{90}{2} = 45[/tex]
f)
[tex]Obw = \sqrt{32} + 2\sqrt{3} + 2\sqrt{2} + 2 = 4\sqrt{2} + 2\sqrt{3} + 2\sqrt{2} + 2 = 2 + 6\sqrt{2} + 2\sqrt{3}[/tex]
[tex]P = \frac{(2\sqrt{2} + \sqrt{32}) * 2}{2} = \frac{(2\sqrt{2} + 4\sqrt{2}) * 2}{2} = \frac{6\sqrt{2}*2}{2} = 6\sqrt{2}[/tex]
