I am a math teacher in Asia. In one math question there are two triangles, A and B. I want to ask which has the larger area. Should I ask:
"Which area of triangle a or triangle b is larger"?
"Which triangle, a or b, has a larger area"?
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@tchrist is correct, for two triangles one has a larger area (we are assuming they don't have the same area). Hence Erik Kowal's, larger vs. largest is most definitely not pedantic.
Although using the word largest and most of the responses here would likely be understood by the hearer/reader. The phrase:
Which triangle has the larger area, triangle a or triangle b?"
is excellent grammar, leaves no room for misunderstanding and more importantly, demonstrates good understanding of English.
"Which triangle, a or b, has the largest area?" unambiguously means what it says. (Note the slight modification of your wording.)
"Which area of triangle a or triangle b is larger?" makes it sound as though triangles a and b have been subdivided into smaller areas, and you are asking which of those areas in each triangle is the largest.