Wysokość ściany bocznej
[tex] {3}^{2} + {x}^{2} = {7}^{2} \\ 9 + {x}^{2} = 49 \\ {x}^{2} = 40 \\ x = \sqrt{40} \\ x = \sqrt{4 \times 10} \\ x = 2 \sqrt{10} cm[/tex]
Pole podstawy
[tex]6 \times \frac{ {6}^{2} \sqrt{3} }{4} = 6 \times \frac{36 \sqrt{3} }{4} = 6 \times 9 \sqrt{3} = 54 \sqrt{3} {cm}^{2} [/tex]
Pole boczne
[tex]6 \times \frac{6 \times 2 \sqrt{10} }{2} = 6 \times \frac{12 \sqrt{10} }{2} = 6 \times 6 \sqrt{10} = 36 \sqrt{10} {cm}^{2} [/tex]
Pole powierzchni całkowitej
[tex] \boxed{ \large{(54\sqrt{3} + 36 \sqrt{10} ) {cm}^{2} }}[/tex]
