Consider △ DGA and △ AED
We know that both the triangles have the same base AD and lie between the parallel lines AD and EG.
So we get
Area of △ DGA = Area of △ AED ……. (1)
Consider △ DBC and △ BFD
We know that both the triangles have the same base DB and lie between the parallel lines BD and CF.
So we get
Area of △ DBF = Area of △ BCD ……. (2)
By adding both the equations
Area of △ DGA + Area of △ DBF = Area of △ AED + Area of △ BCD
By adding △ ABD both sides
Area of △ DGA + Area of △ DBF + Area of △ ABD = Area of △ AED + Area of △ BCD + Area of △ ABD
So we get
Area of △ DGF = Area of pentagon ABCDE
Therefore, it is proved that ar (pentagon ABCDE) = ar (△ DGF).