The Arena's are flippin ENOURMOUS! HOW do they afford/manage it all? And WHY do they make them so big?

Hard to believe nobody is talking about how gigantic the arenas are. Like, apparently it takes days to a week worth of hiking to reach the edge. Like Katniss took three days walking in what seemed to be the same direction to find her pond, in the movie they decided to make that the edge of the arena, it may well have been even bigger in the book. In the Catching fire exert Haymitch took what seemed to be 10 days to find the forcefield at the edge. Even in the 75th games, the relatively small arena is still huge. Meaning, if someone heard the premise of an all stars battle royale TV show they would not expect an arena so large that it took like 6 hours to reach the edge at a fast walk pace. So I guess.

75th Hunger games: Arena was 30km radius, maybe, that would make it 60 km wide. Assume its a circle, it would be about 96km in circumferance, and therefore each of its sectors would be about 8km wide near the edge. This makes sense given it took most of the whole hour to get away from the fog.

74th Games arena: Even bigger, Katniss is headed in the same direction after the bloodbath for about 2.5 days. The first day, lets say she runs at 10km/hr for 2 hours, then 7km/hr for another 4. She would be 48km from the cornucopia, cause she implied she was running in the same direction. 30km at least. If she managed another 20km the second day and 15km the third, that would be an arena that extended at least 65km from the cornucpia at least. In the movie, they decided to make it the edge of the arena near where she got to on the 3rd day. So we will take it that this arena was 65-100km radius, or 130-200 kilometers wide.

50th games arena: I dont know how long Haymitch had the idea to use the edge of the arena, but his games seemed to have lasted about 10 days, and he was walking towards te edge of the arena for what seemed to be a week with Maysilee. But, they also had to sort out logistical issues and Maysilees reluctance, let's say 20km a day, implying a 140km radius, 280 km wide arena.

Does anybody realize how big these arena's are? All of these are conservative estimates. They could have been much bigger too. And this whole ginourmous area is supposed to be rigged with traps and cameras, watched by gammakers, populated by mutant animals, surrounded with a force field, how the heck do they do it? Even though they can, why do they bother to make them so big?