How to Calculate Maximum Polyhexagons in a Given Area?

[ctytrungloi]

I want to calculate number of polyhexagon that can be drawn in a given area (lenght X breadth). Let suppose the side of each hexagon be 'd'.

e.g.,
Case 1: If length, l = 100 cm & breadth, b = 500 cm.
and side of each hexagon, d = 5 cm. Then what will be the maximum number of polyhexagon, n, that can be created in the given region ?

Case 2: If length, l = 100 cm & breadth, b = 500 cm.
and side of each hexagon, d = 10 cm. Then what will be the maximum number of polyhexagon, n, that can be created in the given region ?

Case 3: If length, l = 500 cm & breadth, b = 200 cm.
and side of each hexagon, d = 7 cm. Then what will be the maximum number of polyhexagon, n, that can be created in the given region ?

Case 4: If length, l = 500 cm & breadth, b = 200 cm.
and side of each hexagon, d = 17 cm. Then what will be the maximum number of polyhexagon, n, that can be created in the given region ?

What will be the generalized formula for solving such type of scenario ?


Thanks in advance
Vikas

 

[pat_connell]

The formula for calculating the maximum number of hexagons in a given area (length x breadth) is: n = floor(2*(l/d)*(b/d)). In your examples, the maximum numbers of hexagons would be: Case 1: 200 Case 2: 100 Case 3: 140 Case 4: 58