Answer:
The surface area of the hexagonal pyramid is 291.93 cm2
Step-by-step explanation:
The complete question is
Given -
Base area of pyramid = 166.3 cm2
Height of the pyramid = 12 cm
Surface area of hexagonal pyramid is
[tex]A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{A_B*(6h^2+\sqrt{3} A_B)+A_B}[/tex]
Here AB is the base area and h is the height
Substituting the given values we get
[tex]A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{166.3*(6*12^2+\sqrt{3} * 166.3)+166.3}\\A = \frac{1}{3} * 2 * \sqrt{(166.3 *1152.04)+166.3)}\\A = \frac{2}{3} * 437.893\\A = 291.93 }[/tex]
The surface area of the hexagonal pyramid is 291.93 cm2
