In this case, there are two ways to compute the area, analytically  and by using the computational geometry
Shor, "Applications of random sampling in computational geometry
, II," Discrete & Computational Geometry
16th Canadian Conference on Computational Geometry
, Montreal, Quebec, Canada, 2004, pp.
Discrete & Computational Geometry
, 34(4):679-695, 2005.
Caption: Martin Demaine (left) and his son Erik have drawn on mathematics and computational geometry
to design fonts that incorporate puzzles.
Toussaint, "New results in computational geometry
relevant to pattern recognition in practice," In Pattern Recognition in Practice II, E.
Shewchuk, "Triangle: engineering a 2D quality mesh generator and delaunay triangulator," in Proceedings of the Workshop on Applied Computational Geometry
, Towards Geometric Engineering (FCRC/WACG96), pp.
This was a broad studied problem so now we know many computational geometry
algorithms that can calculate it with O(N [??] log(N)) complexity.
A simple algorithm for homeomorphic surface reconstruction, in Proceedings of the Sixteenth Annual Symposium on Computational Geometry
(Clear Water Bay, Kowloon, Hong Kong, June 12-14, 2000).
The papers are grouped by 6 topics: computer algebra systems, computational geometry
, computer graphics and virtual reality, future information system technologies, mobile sensors, and software development processes.
van de Panne, "Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree", Computational Geometry
: Theory and Applications, 43(1), pages 42-58, 2010