[tex]Zadanie\\\\a-\ krawedz\ szescianu\\\\1.-FALSZ\\\\Graniastoslup\ I\\\\H_1=\frac{1}{2}a\\\\V_1=P_p\cdot H_1=a^2\cdot\frac{1}{2}a=\frac{1}{2}a^3\\\\Graniastoslup\ II\\\\ H_2=a\\\\V_2=P_p\cdot H_2=\frac{1}{2}\cdot a\cdot a\cdot a=\frac{1}{2}a^3\\\\ V_1=V_2[/tex]
[tex]2.\ FALSZ\\\\Graniastoslup\ I\\\\H_1=\frac{1}{2}a\\\\ P_c_1=2P_p_1+P_b_1 = 2\cdot a^2+4\cdot a\cdot\frac{1}{2}a=2a^2+2a^2=4a^2 \\\\Graniastoslup\ II\\\\ b=a\sqrt{2}\\H_2=a\\\\P_c_2=2P_p_2+P_b_2=2\cdot \frac{1}{2}\cdot a\cdot a+2\cdot a\cdot a+a\cdot a\sqrt{2}=a^2+2a^2+a^2\cdot\sqrt{2}=\\\\=3a^2+a^2 \cdot\sqrt{2}=a^2(3+\sqrt{2})\\\\\\P_c_1<P_c_2\\\\4a^2<a^2(3+\sqrt{2})[/tex]
