Question

Find the surface area of the hexagonal pyramid. The base area is 166.3 cm2.

Answer 1

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

$A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{A_B*(6h^2+\sqrt{3} A_B)+A_B}$

Here AB is the base area and h is the height

Substituting the given values we get

$A=\frac{1}{3} * 3^{\frac{3}{4}}*\sqrt{166.3*(6*12^2+\sqrt{3} * 166.3)+166.3}\\A = \frac{1}{3} * 2 * \sqrt{(166.3 *1152.04)+166.3)}\\A = \frac{2}{3} * 437.893\\A = 291.93 }$

The surface area of the hexagonal pyramid is 291.93 cm2