[tex]Podstawa~~ostroslupa~~-romb\\Aby~~obliczyc~~Pp~~czyli~~rombu~~musze~~obliczyc~~jego~~wysokosc.\\Skorzystam~~z~~zaleznosci~~dlugosci~~w~~\Delta~~30^{o} ,60^{o} ,90^{o}~~(rysunek~~w~~zalaczniku) .\\\\a=4 [j]~~-dlugosc~~boku~~rombu\\2\cdot b =4~~\Rightarrow~~b=2[j]\\h=b\sqrt{3} ~~\land~~b=2~~\Rightarrow~~h=2\sqrt{3}[j] \\\\P_{p} =P_{rombu} =a\cdot h \\\\P_{p} =4[j]\cdot 2\sqrt{3} [j]\\\\P_{p} =8\sqrt{3} ~[j^{2} ]\\\\[/tex]
[tex]Szukana~~jest~~wysokosc~~ostroslupa~~\\H-wyoskosc~~ostroslupa\\P_{p} =8\sqrt{3} ~[j^{2} ]\\V=16~[j^{3} ]\\\\V= \dfrac{1}{3} \cdot P_{p} \cdot H~~\mid \cdot 3\\\\H\cdot P_{p}= 3V~~\mid \div P_{p}\\\\H= \dfrac{3V}{P_{p}} \\\\H =\dfrac{3\cdot 16}{8\sqrt{3} }~~[\dfrac{[j^{3} ]}{[j^{2} ]} ]\\\\H=\dfrac{6}{\sqrt{3} } \cdot \dfrac{\sqrt{3} }{\sqrt{3} } ~~[j]\\\\\\H=2\sqrt{3} ~[j]\\\\Odp:~~Wysokosc~~ostroslupa~~wynosi~~2\sqrt{3} ~[j].[/tex]
