Zad. 1
[tex]d=a\sqrt2\\a\sqrt2=12cm /:\sqrt2\\a=\frac{12}{\sqrt2}cm=\frac{12\sqrt2}2cm=6\sqrt2cm[/tex]
[tex]Pp=a^2=(6\sqrt2cm)^2=36*2cm^2=72cm^2[/tex]
[tex](\frac12d)^2+H^2=b^2\\(6cm)^2+H^2=(10cm)^2\\36cm^2+H^2=100cm^2 /-36cm^2\\H^2=64cm^2\\H=8cm[/tex]
[tex]V=\frac13PpH\\V=\frac{72cm^2*8cm}3=24cm^2*8cm=192cm^3[/tex]
Odp. Falsz
Zad. 2
[tex]b=6dm\\\alpha=30^\circ\\2H=b\\2H=6dm /:2\\H=3dm\\\\\frac12d=H\sqrt3\\\frac12d=3\sqrt3dm /*2\\d=6\sqrt3dm\\\\6\sqrt3dm =a\sqrt2/:\sqrt2\\a=\frac{6\sqrt3}{\sqrt2}dm=\frac{6\sqrt6}2dm=3\sqrt6\\\\Pp=(3\sqrt6dm)^2=9*6dm^2=54dm^2\\V=\frac13PpH\\V=\frac13*54dm^2*3dm=54dm^3[/tex]