Delphi image canvas... paint an area (triangle, rectangle, polygons)

As a complement to TLama's excellent answer, this is a case where you can obtain pretty convenient syntax using the open array construct. Consider the helper function

procedure DrawPolygon(Canvas: TCanvas; const Points: array of integer);
var
  arr: array of TPoint;
  i: Integer;
begin
  SetLength(arr, Length(Points) div 2);
  for i := 0 to High(arr) do
    arr[i] := Point(Points[2*i], Points[2*i+1]);
  Canvas.Polygon(arr);
end;

defined and implemented once and for all. Now you can do simply

Canvas.Pen.Width := 2;
Canvas.Pen.Color := clRed;
Canvas.Brush.Color := clYellow;
DrawPolygon(Canvas, [5, 5, 55, 5, 30, 30]);

to draw the same figure as in TLama's example.

Use the TCanvas.Polygon function. Declare an array of TPoint, set its length to the count of your points, specify each point's coordinates (optionally modify canvas pen and/or brush) and pass this array to the TCanvas.Polygon function. Like in this boring example:

procedure TForm1.Button1Click(Sender: TObject);
var
  Points: array of TPoint;
begin
  SetLength(Points, 3);
  Points[0] := Point(5, 5);
  Points[1] := Point(55, 5);
  Points[2] := Point(30, 30);
  Canvas.Pen.Width := 2;
  Canvas.Pen.Color := clRed;
  Canvas.Brush.Color := clYellow;
  Canvas.Polygon(Points);
end;

Here's how it looks like:

As a complement to both TLama's and Andreas answer, here's another alternative :

procedure TForm1.Button1Click(Sender: TObject);
begin
  Canvas.Pen.Color := clRed;
  Canvas.Brush.Color := clYellow;
  Self.Canvas.Polygon( [Point(5,5), Point(55,5), Point(30,30)]);
end;

Utilizing open array construct and Point record.