Given:
[tex]\begin{gathered} Base\text{ \lparen a\rparen = 2 cm} \\ Height\text{ \lparen h\rparen = 6 cm} \end{gathered}[/tex]
Required:
The surface area of a hexagonal pyramid.
Explanation:
The surface area of the hexagonal pyramid with base a and a height h is given as,
[tex]\begin{gathered} Area\text{ = }\frac{3\sqrt{3}}{2}a^2\text{ + 3a }\sqrt{h^2}\text{ + }\frac{3a^2}{4} \\ \end{gathered}[/tex]
Substituting the given value in the formula,
[tex]\begin{gathered} Area\text{ = }\frac{3\sqrt{3}}{2}\times\text{ \lparen2\rparen}^2\text{ + 3}\times2\times\sqrt{6^2\text{ + }\frac{3\times2^2}{4}} \\ Area\text{ = 47.86229} \\ Area\text{ }\approx\text{ 47.86 cm}^2 \end{gathered}[/tex]
Answer:
Thus the surface area of the given hexagonal pyramid is 47.86 sq.cm.
