function area = triangle_area_2d ( t )

%*****************************************************************************80
%
%% TRIANGLE_AREA_2D computes the area of a triangle in 2D.
%
%  Discussion:
%
%    If the triangle's vertices are given in counterclockwise order,
%    the area will be positive.  If the triangle's vertices are given
%    in clockwise order, the area will be negative!
%
%    An earlier version of this routine always returned the absolute
%    value of the computed area.  I am convinced now that that is
%    a less useful result!  For instance, by returning the signed 
%    area of a triangle, it is possible to easily compute the area 
%    of a nonconvex polygon as the sum of the (possibly negative) 
%    areas of triangles formed by node 1 and successive pairs of vertices.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    17 October 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, real T(2,3), the triangle vertices.
%
%    Output, real AREA, the area of the triangle.
%
  area = 0.5 * ( ...
      t(1,1) * ( t(2,2) - t(2,3) ) ...
    + t(1,2) * ( t(2,3) - t(2,1) ) ...
    + t(1,3) * ( t(2,1) - t(2,2) ) );

  return
end
