Consider △ ABD
We know that
Area of △ ABD = ½ × BD × AE
In the same way
Area of △ ADC = ½ × DC × AE
From the figure we know that D is the median
So we get
BD = DC
We know that
Area of △ ABD = ½ × BD × AE
It can be written as
Area of △ ABD = ½ × DC × AE
So we get
Area of △ ABD = Area of △ ADC
Therefore, it is proved that a median divides a triangle into two triangles of equal area.