[tex]zad.1\\\\V= P_{p} \cdot H~~\land ~~H=15~cm\\\\a)~~graniastoslup~~prawidlowy~~trojkatny~~\Rightarrow~~podstawa~~jest~~trojkat~~rownoboczny\\\\P_{p} =P\Delta_{rownoboczny} =\dfrac{a^{2} \sqrt{3} }{4} ~~\land~~a=6~cm\\\\P_{p} =\dfrac{(6cm)^{2} \sqrt{3} }{4}=9\sqrt{3} ~cm^{2} \\\\V=9\sqrt{3} ~cm^{2} \cdot 15~cm=135\sqrt{3} ~cm^{3} \\\\b)~~granistoslup~~prawidlowy~~czworokatny ~~\Rightarrow ~~podstawa~~jest~~kwadrat\\\\P_{p} =P_{kwadrat} =a^{2} ~~\land~~a=6 cm\\\\P_{p}=36~cm^{2} \\\\[/tex]
[tex]V=36~cm^{2} \cdot 15~cm=540~cm^{3}[/tex]
[tex]c)~~granistoslup~~prawdlowy~~szesciokatny~~\Rightarrow~~podstawa~~jest~~szesciokat\\\\P_{p} =6\cdot P\Delta _{rownoboczny}=6\cdot \dfrac{a^{2} \sqrt{3} }{4} ~~\land~~a=6~cm\\\\P_{p} =6\cdot \dfrac{(6cm)^{2} \sqrt{3} }{4}=54\sqrt{3} ~cm^{2} \\\\V=54\sqrt{3} ~cm^{2} \cdot 15~cm=810\sqrt{3} ~cm^{3}[/tex]
