Krawędź podstawy
[tex]24cm \div 6 = 4cm[/tex]
Krawędź boczna
[tex]18 - 4 = 14 cm\\ \\ 14 \div 2 = 7cm[/tex]
Wysokość ściany bocznej
[tex] {2}^{2} + {x}^{2} = {7}^{2} \\ 4 + {x}^{2} =49 \\ {x}^{2} = 45 \\ x = \sqrt{45} \\ x = \sqrt{9 \times 5} \\ x = 3 \sqrt{5} cm[/tex]
Pole podstawy
[tex]6 \times \frac{ {a}^{2} \sqrt{3} }{4} = 6 \times \frac{ {4}^{2} \sqrt{3} }{4} = 6 \times \frac{16 \sqrt{3} }{4} = 6 \times 4 \sqrt{6} = 24 \sqrt{3} {cm}^{2} [/tex]
Pole boczne
[tex]6 \times \frac{4 \times 3 \sqrt{5} }{2} = 6 \times \frac{12 \sqrt{3} }{2} = 6 \times 6 \sqrt{3} = 36 \sqrt{3} {cm}^{2} [/tex]
Pole powierzchni całkowitej
[tex]24 \sqrt{3} {cm}^{2} + 36 \sqrt{3} {cm}^{2} = \boxed{ \underline{60 \sqrt{3} {cm}^{2} }}[/tex]