What is API REST call to get projects associated to a rapidboard?
There is no actual project associated to a rapidboard. A JQL is associated with a rapidboard.
GET /rest/greenhopper/1.0/rapidview/list
This should list down all the rapidboards and the query object is what you're looking for.
I guess the next question is: how do I get hold of the JQL behind a rapidboard?
GET /rest/greenhopper/1.0/rapidviewconfig/editmodel.json?rapidViewId={BOARDID} and look for filterconfig -> query
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