Area calculation for non-triangle face of a surface mesh

[TomTheVercetti]

Hi CGAL community,
I want to calculate area of a mesh face, which in this example is a 5by5 rectangle:

I expect 25 as a result but I get 12.5.

Can you please explain why?

This is my full code:

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Triangulation_3.h>
#include <CGAL/Polygon_mesh_processing/measure.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/intersections.h>
#include <vector>
#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef CGAL::Simple_cartesian<double> K;
typedef CGAL::Surface_mesh<K::Point_3> Mesh;
typedef Mesh::Vertex_index vertex_descriptor;
typedef Mesh::Face_index face_descriptor;
typedef K::Point_3 Point_3;

int main()
{

    // Create mesh -----------------------------------------------------------------------------------------------------
    Mesh mesh;
    vertex_descriptor v0 = mesh.add_vertex(K::Point_3(0, 0, 0));
    vertex_descriptor v1 = mesh.add_vertex(K::Point_3(5, 0, 0));
    vertex_descriptor v2 = mesh.add_vertex(K::Point_3(5, 5, 0));
    vertex_descriptor v3 = mesh.add_vertex(K::Point_3(0, 5, 0));
    // create a quad
    face_descriptor f1 = mesh.add_face(v0, v1, v2, v3);

    // Print the basic statistics and info ----------------------------------------------------------------------------
    double area_f1 = CGAL::Polygon_mesh_processing::face_area(f1, mesh);
    std::cout << "Area of face f1: " << area_f1 << std::endl;
    return 0;
}

[stla]

The doc for face_area says: "computes the area of a face of a given triangulated surface mesh".