From the figure we know that median of a triangle divides it into triangles of equal area
We know that AO is the median of △ ACD
It can be written as
Area of △ COA = Area of △ DOA ……. (1)
We know that BO is the median of △ BCD
It can be written as
Area of △ COB = Area of △ DOB ……. (2)
By adding both the equations
Area of △ COA + Area of △ COB = Area of △ DOA + Area of △ DOB
So we get
Area of △ ABC = Area of △ ABD
Therefore, it is proved that ar (△ ABC) = ar (△ ABD).