Some other ideas are this ...
Use D3DXVec3Project to take each point of a triangle and project it to screen space.
Take the cross product of any two screen space triangle points. This is twice the area of the triangle (in screen space).
Thanks very much. As the area is computed without D3D or OPENGL, I must write my own rasterizer.
I wonder if the triangles can be paremeterized into a vector, like spherical harmonics way. And the vector can by projected on a plane. Is there some ways.