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(4*2sqrt3)/2 = 6*4sqrt3 = 24sqrt3 unit squared 

the lateral area = 4*4*6/2 = 4*2*6 = 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 = [tex]\frac{1}{2}[/tex] (side of base) × slant height

                                    = [tex]\frac{1}{2}[/tex] × 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 = [tex]\frac{360}{\text{number of sides}}[/tex] ]

and ∠CAD = 30°

Now tan 30° = [tex]\frac{DC}{AD}[/tex] = [tex]\frac{2}{AD}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{2}{AD}[/tex]

AD = [tex]2\sqrt{3}[/tex]

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

6 × [[tex]\frac{4}{2}[/tex] × [tex]2\sqrt{3}[/tex]] =  [tex]24\sqrt{3}[/tex]

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

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