Doesn't compute for me

 If the hijab and burka are not mandated in the Koran, and I have read they are not, then they must be worn for modesty, no?  And if girls only start wearing it at puberty, does it not have something to do with sexual modesty?  If not, what else?  This picture is why I can't square the modesty circle with the hijab:

This young woman is not scrub-faced, but rather heavily made up, presumably to be attractive to the opposite sex, no?  Frankly, the whole thing mystifies me?  If hair is sexual and has to be covered, why is makeup OK?

Lots of question marks in this piece, but most of them are rhetorical.