Answer:
(B) [tex]SA=79.18m^2[/tex]
Step-by-step explanation:
It is given from the figure, the side of the regular hexagonal pyramid is 3 m, slant height is 6.2 m and height is 5.6 m.
The formula for Surface area of the regular hexagonal pyramid is:
[tex]SA=\frac{pl}{2}+B[/tex]
where B is the area of the base, p is the perimeter and l is the slant height.
Now, the perimeter can be found as:
[tex]P=6{\times}3[/tex]
[tex]P=18 m[/tex]
And, the area of the base is:
[tex]B=\frac{3\sqrt{3}s^2}{2}[/tex]
Substituting the value of s in the above formula, we get
[tex]B=\frac{3\sqrt{3}(3)^2}{2}[/tex]
[tex]B=23.382m^2[/tex]
Now, substituting the values of B, and P in the formula of Surface area, we get
[tex]SA=\frac{18{\times}6.2}{2}+23.382[/tex]
[tex]SA=79.18m^2[/tex]
Thus, the Surface area of the regular hexagonal pyramid is [tex]79.18m^2[/tex].
Hence, option B is correct.
