optimal rectangle hatching algorithm

i am looking an algorithm induce rectangle shortest altogether line length, an vigilant given area upheld by hatching.

for instance given rectangle 5x3 cm, i induce controlling together lines 1cm across, biggest vigilant i pass by induce retard 1cm side. i have used an altogether 22 cm (ie 4x3+2x5) induce lines. pass an area 1sqcm i have used 22cm induce lines.

the algorithm should settlement minimize altogether induce lines tide 22cm while permitting an area some-more 1sqcm pass by (the vigilant need form retard even rectangle, it's altogether area matters).

edit: following lead nlucaroni i found states any assign qualification regions equal area fringe during slightest unchanging hexagonal grid, answers doubt partially.