Answer:
The total surface area of a regular hexagonal pyramid is 146.2 cm².
Step-by-step explanation:
The base is a regular hexagon 4cm on a side. its height is 8 cm.
The total surface area of a pyramid with regular hexagon base
[tex]A=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}[/tex]
Where, a represents the base edge and h represents the height of the pyramid.
The area of given regular hexagonal pyramid is
[tex]A=\frac{3\sqrt{3}}{2}(4)^2+3(4)\sqrt{(8)^2+\frac{3(4)^2}{4}[/tex]
[tex]A=\frac{3\sqrt{3}}{2}(16)+12\sqrt{64+12}[/tex]
[tex]A=24\sqrt{3}+12\sqrt{76}[/tex]
[tex]A=146.182794027[/tex]
[tex]A=146.2[/tex]
The total surface area of a regular hexagonal pyramid is 146.2 cm².
