Question

What is the volume of a regular hexagonal prism with a side length of 4 and a height of 9? Please give the answer as square root. PLEASE HELP ASAP!!

Answer 1

The height of an equilateral triangle with side s is s*sqrt(3)/2
The area of an equilateral triangle is therefore s^2*sqrt(3)/4
The area of a hexagon with side s is 6 times the area of an equilateral triangle
=6*s^2*sqrt(3)/4
=3s^2*sqrt(3)/2
 
Here s=4, 
Area of base (hexagon) = 3*4^2*sqrt(3)/2=24sqrt(3)
Volume of prism
=(base area)*height
=24sqrt(3)*9
=216sqrt(3)