Verified Answer :

jhonyy9

for get the length of apothem write sin60 = a/4 so sqrt3 /2 = a/4 so a = 4sqrt3 /2

a = 2sqrt3 

so area of base = 6(42sqrt3)/2 = 64sqrt3 = 24sqrt3 unit squared 

the lateral area = 446/2 = 426 = 48 unit squared 

total area = 24sqrt3 +48 = 24(sqrt3 +2) unit squared 

 hope this will help you

Answer:

113.57 unit²

Step-by-step explanation:

Surface area of a pyramid with regular hexagonal base

= Area of slant sides + area of Hexagonal base

Area of one slant side = \(\frac{1}{2}\) (side of base) × slant height

                                    = \(\frac{1}{2}\) × 6 × 4

                                    = 3 × 4

                                    = 12 unit²

Since hexagonal pyramid has 6 slant sides.

So area of sic slant sides = 6 × 12 = 72 unit²

Now for the area of hexagonal base we will take triangle ABC.

∠BAC = 60°    [angle formed at center = \(\frac{360}{\text{number of sides}}\) ]

and ∠CAD = 30°

Now tan 30° = \(\frac{DC}{AD}\) = \(\frac{2}{AD}\)

\(\frac{1}{\sqrt{3}}=\frac{2}{AD}\)

AD = \(2\sqrt{3}\)

Now hexagonal base area = 6 × [\(\frac{1}{2}\) (BC)(AD)]

6 × [\(\frac{4}{2}\) × \(2\sqrt{3}\)] =  \(24\sqrt{3}\)

Therefore area of the pyramid = 72 + 41.57 = 113.57 unit²