We studied the problem of finding planar regions in a triangulated terrain. For a set of points in 3-space, we construct the Delaunay triangulation. Then, with two different methods we look for a region which is flat. The first method uses an algorithm to find the largest convex polygon. The algorithm works well on smaller sets of points, but on larger sets of points it performs poorly due to its quadratic time complexity. In the second method, we use an approximation algorithm. It performs better on larger data sets, as well as on real geographical data, which can be obtained on the web portal LIDAR. The implemented interface helps us to test both methods in an easy way and visualize the results.