[tex]Zadanie\\\\a-krawedz\ podstawy\\\\2a-wysokosc\ sciany\ bocznej\\\\H=?\\\\ P_c= P_p+P_b=a^2+4\cdot\frac{1}{2}\cdot a\cdot h \\\\a^{2}+4\cdot\frac{1}{2}\cdot a\cdot2a=80\\\\a^2+2\cdot2a^2=80\\\\5a^2=80\ \ \mid:5\\\\a^2 =16\\\\a= 4\ (j)[/tex]
[tex]Obliczam\ wysokosc\ H\ ostroslupa\ (tw.\ Pitagorasa)\\\\a_1=\frac{1}{2}a=\frac{1}{2} \cdot4=2\\\\c=h=2a=2\cdot4=8\\\\b=H=?\\\\a_1^2+b^2=c^2\\\\2^2+b^2= 8^2\\\\ 4+b^2=64\ \ \mid-4\\\\b^2=60\\\\b=\sqrt{60}\\\\b=2\sqrt{15}\ (j)\\\\H=b= 2\sqrt{15}\ (j)\\\\ Obliczam\ objetosc\\\\V=\frac{1}{3}\cdot P_p\cdot H=V=\frac{1}{3}\cdot a^2\cdot H\\\\V=V=\frac{1}{3}\cdot 4^2\cdot2\sqrt{15}=V=\frac{1}{3}\cdot 16\cdot2\sqrt{15} =\frac{32\sqrt{15} }{3}\ (j^2)[/tex]
