graniastosłup prawidłowy czworokątny ma w podstawie kwadrat
d=8
\alpha=30
P_c=2*P_p+P_b=2a^2+4*a*H
\sin\alpha=\frac{c}{d}
\sin(30)=\frac{c}{8}
\sin(30)=\frac{1}{2}
\frac{1}{2}=\frac{c}{8}
2c=8
c=4 (przekątna kwdratu)
c=a\sqrt{2}
a=\frac{c}{\sqrt{2}}=\frac{8}{\sqrt{2}}=\frac{8*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=\frac{8\sqrt{2}}{2}=4\sqrt{2}
\cos(30)=\frac{H}{d}
\frac{\sqrt{3}}{2}=\frac{H}{8}
2H=8\sqrt{3}
H=4\sqrt{3}
P_c=2a^2+4*a*H=2*(4\sqrt{2})^2+4*4\sqrt{2}*4\sqrt{3}=32+64\sqrt{6}=32(1+2\sqrt{6})cm^2
V=P_p*H=(4\sqrt{2})^2*4\sqrt{3}=128\sqrt{3}cm^3