1.
[tex]a=5\\h=8\\\\Pb=4*\frac{ah}2=2ah=2*5*8=10*8=80\\Pc=Pb+Pp=80+5*5=80+25=105\\Odp. C[/tex]
2.
Czworoscian foremny to ostroslup skladajacy sie z czterech jednakowych trojkatow rownobocznych.
[tex](\frac13h)^2+H^2=h^2\\H^2=h^2-(\frac13h)^2\\\\h=\frac{a\sqrt3}2\\H^2=(\frac{a\sqrt3}2)^2-(\frac13*\frac{a\sqrt3}2)^2\\H^2=\frac{3a^2}4-\frac{3a^2}{36}\\H^2=\frac{27a^2}{36}-\frac{3a^2}{36}\\H^2=\frac{24a^2}{36}=\frac{2a^2}3\\H=\sqrt{\frac{2a^2}3}=\frac{a\sqrt2}{\sqrt3}*\frac{\sqrt3}{\sqrt3}=\frac{a\sqrt6}3\\\\H=\frac{20\sqrt6}3cm[/tex]
3.
[tex]V=\frac13a^2*H\\96cm^3=\frac{a^2}3*18cm\\96cm^3=a^2*6cm /:6cm\\16cm^2=a^2\\a=4cm[/tex]
4.
[tex]d=a\sqrt2\\b=4\sqrt5=d\\a\sqrt2=4\sqrt5 /:\sqrt2\\a=\frac{4\sqrt5}{\sqrt2}=\frac{4\sqrt{10}}2=2\sqrt{10}\\\\(\frac12d)^2+H^2=b^2\\(2\sqrt5)^2+H^2=(4\sqrt5)^2\\4*5+H^2=16*5\\20+H^2=80 /-20\\H^2=60\\H=\sqrt{60}=\sqrt{4*15}=2\sqrt{15}\\\\V=\frac13a^2*H\\V=\frac13*(2\sqrt{10})^2*2\sqrt{15}\\V=\frac13*40*2\sqrt{15}\\V=\frac{80\sqrt{15}}3[/tex]
