What you want is a 2D coordinate system in the plane of intersection, then you can use your equation for area. Assume that your original points are represented as vectors {Vk} from some origin O (this is your original 3D coordinate system). As you have the equation of the plane, choose one point on it as the new origin Op, and choose two orthogonal unit vectors (U1, U2) that lie in the plane as the new axes. (i.e. choose two orthogonal vectors orthogonal to the normal of the plane) Then in your new coordinate system, the 2D coordinates of the point Vk are: ( (Vk-Op).U1, (Vk-Op).U2 ) i.e. you simply project the 3D vector from your new origin onto your new axes. Note - this includes Alan's solution, the vectors U1 and U2 would be rows of his rotation matrix. It's just a different way of looking at things.
Peter "Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."