Pole podstawy
[tex]Pp = \frac{ {4}^{2} \sqrt{3} }{4} = \frac{16 \sqrt{3} }{4} = 4 \sqrt{3} {cm}^{2} [/tex]
Wysokość graniastosłupa
[tex] {4}^{2} + {H}^{2} = {12}^{2} \\ 16 + {H}^{2} = 144 \\ {H}^{2} = 128 \\ H = \sqrt{128} \\ H = \sqrt{64 \times 2} \\ H = 8 \sqrt{2} cm[/tex]
Objętość
[tex]V = 4 \sqrt{3} \times 8 \sqrt{2} = \boxed{\underline{32 \sqrt{6} {cm}^{3} }}[/tex]
Pole boczne
[tex]3(4 \times 8 \sqrt{2} ) = 3 \times 32 \sqrt{2} = \boxed{\underline{96 \sqrt{2} {cm}^{2} }}[/tex]
