Drawing any rectangle to a GTK+ DrawingArea fills the whole DrawingArea

I have a GTK+ DrawingArea that should display a rectangle in the top left corner. When I draw the rectangle using Cairo, the whole drawing area is filled with the color of the rectangle. How can I prevent that? Why does Cairo do that? What am I doing wrong?

#include <gtkmm.h>

class Window : public Gtk::Window
{
  private:
    Gtk::DrawingArea area;

    bool on_area_expose(GdkEventExpose* event)
    {
      Gtk::Allocation allocation = area.get_allocation();
      Cairo::RefPtr<Cairo::Context> context =
          area.get_window()->create_cairo_context();
      int width = allocation.get_width();
      int height = allocation.get_height();
      context->set_source_rgba(0, 0, 0, 1);
   开发者_运维技巧   context->rectangle(0, 0, double(width)/10, double(height)/10);
      context->paint();
      return true;
    }

  public:
    Window() : Gtk::Window()
    {
      area.signal_expose_event().connect(
        sigc::mem_fun(*this, &Window::on_area_expose));
      add(area);
    }
};

int main(int argc, char* argv[])
{
  Gtk::Main app(argc, argv);
  Window window;
  window.show_all();
  Gtk::Main::run(window);
  return 0;
}

I compiled the code using

g++ gtktest.cpp `pkg-config --libs --cflags gtkmm-2.4` -o gtktest

context->paint() paints the current source everywhere within the current clip region. The proper method to call is Gtk::Context::fill.