This second custom triangle example shows an alternative implementation for a custom shape, showing a partial specialization for the area calculation.
#include <iostream>
#include <boost/array.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/geometry/io/dsv/write.hpp>
template <typename P>
struct triangle : public boost::array<P, 3>
{
};
namespace boost { namespace geometry { namespace dispatch {
template<typename Point>
struct area<triangle<Point>, ring_tag>
 
{
    template <typename Strategy>
    static inline double apply(triangle<Point> const& t, Strategy const&)
    {
        return 0.5  * ((get<0>(t[1]) - get<0>(t[0])) * (get<1>(t[2]) - get<1>(t[0]))
                     - (get<0>(t[2]) - get<0>(t[0])) * (get<1>(t[1]) - get<1>(t[0])));
    }
};
}}} 
int main()
{
    
    triangle<boost::tuple<double, double> > t;
    t[0] = boost::make_tuple(0, 0);
    t[1] = boost::make_tuple(5, 0);
    t[2] = boost::make_tuple(2.5, 2.5);
    std::cout << "Triangle: " << boost::geometry::dsv(t) << std::endl;
    
    boost::tuple<double, double> c;
    std::cout << "Centroid: " << boost::geometry::dsv(c) << std::endl;
    return 0;
}