The true surface area of a landscape is greater than its projected (i.e. "flat") surface area. This submission estimates the true surface area of a digital elevation model by calculating the surface area of the eight three-dimensional triangles formed by each cell centre and its eight neighbouring cell centres.
The approach is based on Jenness, Jeff S. 2004. “Calculating Landscape Surface Area from Digital Elevation Models.” Wildlife Society Bulletin 32 (3): 829–839.
Changed function name to reflect file name, added image illustrating the approach