This mathematical observation deals with the development of a completely new expression [(S/4D) × √ {(S₁²-D²)(D²-D₁²)}] to calculate the area of a trapezoid system. Because of the difficulties of the previous methods to find out the area of a trapezoid (AOT), the proposed formula has thus indicated the best way to determine the AOT more precisely and easily beyond limitation, successfully. It is obvious that the derived formula is helpful to determine AOT more easily and precisely rather than existing method. And this developed theorem for the trapezoid system is observed for the first time.