From the figure we know that BE is the median of △ ABD
So we get
Area of △ BDE = Area of △ ABE
It can be written as
Area of △ BDE = ½ (Area of △ ABD) …… (1)
From the figure we know that CE is the median of △ ADC
So we get
Area of △ CDE = Area of △ ACE
It can be written as
Area of △ CDE = ½ (Area of △ ACD) …….. (2)
By adding both the equations
Area of △ BDE + Area of △ CDE = ½ (Area of △ ABD) + ½ (Area of △ ACD)
By taking ½ as common
Area of △ BEC = ½ (Area of △ ABD + Area of △ ACD)
So we get
Area of △ BEC = ½ (Area of △ ABC)
Therefore, it is proved that ar (△ BEC) = ½ ar (△ ABC).