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A prism has a regular hexagonal base whose side is 12 cm. The height of the prism is 24 cm. It is cut into 4 equal parts by 2 perpendicular cuts as shown in figure. What is the sum of the total surface area of the four parts?

A prism has a regular hexagonal base whose side is 12 cm. The height of the prism is 24 cm. It is cut into 4 equal parts by 2 perpendicular cuts as shown in figure. What is the sum of the total surface area of the four parts? Correct Answer 2880 + 1008√3

 

                  

⇒ 432√3 + 1728

Extra surface created = 2 × Area of the rectangle with the line joining the opposite vertices as base + 2 × Area of the rectangle with line cutting the opposite sides into half

⇒ 2 × 2a × h + 2 × √3a × h

⇒ 1152 + 576√3

Total surface area = 432√2 + 1728 + 1152 + 576√3 = 2880 + 1008√3

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