Given pyramid with a regular hexagonal base,
side length=6[tex] \sqrt{3} [/tex] cm
Height = 4 cm
We need to find the area of the hexagonal base. First step is to find the apothm,
a=side*([tex] \sqrt{3}/2 [/tex]
=6*3/2=9
So the area of each equilateral triangle making up the base
=base*apothem/2
=6[tex] \sqrt{3} [/tex] *9/2
=27[tex] \sqrt{3} [/tex]
The area of base = 6 area of each triangle
=6*27[tex] \sqrt{3} [/tex]
=162[tex] \sqrt{3} [/tex]
Volume of pyramid = area of base * height /3
=162[tex] \sqrt{3} [/tex]*4/3
=216[tex] \sqrt{3} [/tex]
