Odpowiedź:
[tex]a)\ \ 3\sqrt{3}\\\\h=\frac{a\sqrt{3}}{2}\\\\3\sqrt{3}=\frac{a\sqrt{3}}{2}\ \ /\cdot2\\\\6\sqrt{3}=a\sqrt{3}\\\\a\sqrt{3}=6\sqrt{3}\ \ /:\sqrt{3}\\\\a=6\\\\Ob=3a\\\\Ob=3\cdot6=18\\\\\\b)\ \ 6\sqrt{6}\\\\h=\frac{a\sqrt{3}}{2}\\\\6\sqrt{6}=\frac{a\sqrt{3}}{2}\ \ /\cdot2\\\\12\sqrt{6}=a\sqrt{3}\\\\a\sqrt{3}=12\sqrt{6}\ \ /:\sqrt{3}\\\\a=12\sqrt{2}\\\\Ob=3a\\\\Ob=3\cdot12\sqrt{2}=36\sqrt{2}[/tex]
[tex]c)\ \ 2\sqrt{2}\\\\h=\frac{a\sqrt{3}}{2}\\\\2\sqrt{2}=\frac{a\sqrt{3}}{2}\ \ /\cdot2\\\\4\sqrt{2}=a\sqrt{3}\\\\a\sqrt{3}=4\sqrt{2}\ \ /:\sqrt{3}\\\\a=\frac{4\sqrt{2}}{\sqrt{3}}\\\\a=\frac{4\sqrt{2}}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{6}}{3}\\\\Ob=3a\\\\Ob=\not3\cdot\frac{4\sqrt{6}}{\not3}=4\sqrt{6}[/tex]
[tex]d)\ \ 4\\\\h=\frac{a\sqrt{3}}{2}\\\\4=\frac{a\sqrt{3}}{2}\ \ /\cdot2\\\\8=a\sqrt{3}\\\\a\sqrt{3}=8\ \ /:\sqrt{3}\\\\a=\frac{8}{\sqrt{3}}\\\\a=\frac{8}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{8\sqrt{3}}{3}\\\\Ob=3a\\\\Ob=\not3\cdot\frac{8\sqrt{3}}{\not3}=8\sqrt{3}[/tex]
Szczegółowe wyjaśnienie:
[tex]Wz\'or\ \ na\ \ wysoko\'s\'c\ \ w\ \ tr\'ojkacie\ \ r\'ownobocznym\\\\h=\frac{a\sqrt{3} }{2}[/tex]
