I did not say it was impossible. I said "измерить" suits better for that particular example. And "измерять" is possible, but it involves some subtle nuances. If speaking in general, "измерить" just sounds more natural in the context provided by Valda.
And as to your examples, Delog: yes, they do work. But there are even more nuances, and your examples do not show all of them.
Consider this one:
Древние Греки догадались, как можно измерить Землю.
but not "измерять"!
I hope you feel the difference. Unfortunately, there is not a simple single rule for the aspect choice.