Given that the internal area of the human mouth is approximately a square, why the vowels pronunciation chart is usually represented by a trapezoid?
The original reason was, "
[ɑ] sound less different than
[u]". It seemed intuitively like there was less "space" between front and back low vowels, so they drew less space on that part of the diagram.
Nowadays, though, the reasons are acoustic.
The position of a vowel on the trapezoid is actually an objective, measurable quantity: the "formant frequencies". There's a longer explanation in this other answer, but the formants are basically a mathematical representation of how our vocal tract is shaping the sound.
A modern vowel diagram plots F1 (the first formant) from top to bottom, and F2-F1 (the difference between the first two formants) from right to left. And this ends up giving the nice, distinctive IPA trapezoid shape!
So there is an objective reason it looks like a trapezoid, it's not just an artifact of early phonetics work. But what is this reason?
In the end, it has to do with the human tongue: when the tongue is raised toward the roof of the mouth (a high vowel), there's a lot of freedom to move it forward and backward (making front and back vowels). When it's lowered (a low vowel), there's not as much freedom. So the space of low vowels is, quite simply, smaller than the space of high vowels.
The physiological reason is that the tongue has a greater front-back range when the tongue is raised, as compare to when it is lowered, especially in that it can go further forward. Earlier, formants were simply plotted F1 vs F2, but the contemporary calculation is based on a modified relation which mimics the articulatory trapezoid.