As far as I am aware, there is no such term as "First Moment of Inertia". The term "Moment of Inertia" is used either in its true sense (ie having the units M.L^2), or is used to refer to the "Second Moment of Area", having the units L^4. Second moment of area is also sometimes called "Area Moment of Inertia". There is also a term "First Moment of Area", which has the units L^2. There are certainly ways to find the Second Moment of Area of any given plane area, about a given axis. But when you say you want to start with what appears to be a true moment of inertia, one needs to ask which moment of inertia you are referring to. For any solid, there are three principle moments of inertia, and in the case of a beam none of them have any special relationship to the second moments of area of any plane section, since they would be heavily dependent on the length of the beam, while the area properties of the section would not. It is possible to define what is known as the moment of inertia of a plane lamina, which is an imaginary object, being infinitely thin yet having a finite mass per unit area, This is about the only object I can think of for which there would be a true correlation between "moment of inertia " and "second moment of area".