BASE AREA OF THE BOX:
Regular hexagon with 2 inch edges contains 180*(6-2) = 180*4 = 720 degrees
That's 120 degrees in each of the corner pockets.
Drawing line segments from the center to each vertex creates 6 congruent isosceles triangles.
Selecting any one of these six triangles and dropping the height from the center to the edge
creates a 30-60-90 right triangle with height equal to the square root of 3 (rad3) and base measure 1.
So the area of each of these triangles is the square root of 3 , or in slang terms "rad 3", which means
the base area is 6*rad3.
The volume of the box is therefore 36*rad3
BASE AREA OF THE CANDY:
Dropping the height from one vertex to the opposite side of this equilateral triangle
creates 2 right triangles with base measure 1/2 and hypotneuse 1. So the height
must be rad3/2. The area of the entire equilateral triangle is rad3/4, which is the base area.
The volume of the candy is rad3/2
36*rad3 divided by rad3/2 =
36 rad3 times 2/rad3 <--- KFC : keep , change, flip
36 * 2 <-- rad3 cancels out
72 candies will fill the box.
