Construct lines AC and BM.
Let us take h as the distance between AB and CD
We know that
Area of △ ACD = ½ × CD × h
In the same way
Area of △ ABM = ½ × AB × h
From the figure we know that AB = CD
So it can be written as
Area of △ ABM = ½ × CD × h
So we get
Area of △ ABM = Area of △ ACD
Let us add △ ACM on both sides
Area of △ ABM + Area of △ ACM = Area of △ ACD + Area of △ ACM
So we get
Area of ABMC = Area of △ ADM
Therefore, it is proved that ar (△ ADM) = ar (ABMC).