I did consider that, but a number system based on 16’s is called hexadecimal, so I went for i instead of a.
And, even more familiarly, a number system based on 10 is called “decimal”. 
But the “deci-” in there does still etymologically derive from a word meaning “a tenth”.
Tri means three, and mestral means months. A trimester is a three month period. (Think about the common division in pregnancy.) While it is used in scholarly circles to refer to a three part system, this is because summer break is itself considered a trimester. It’s the opposite of how a semester works, which literallyrefers to a period of six months, but tends to only refer to a period of four months.
And, no, that doesn’t make it a good term to use, as it still tends to refer to half a year. It’s just that a “school year” is shorter than a real year.