__GIVEN :__ Let ABC be a triangle

whose median intersect side BC

and E is the mid- point

**TO PROVE :***area ( BED ) = 1/4 area ( ABC )*

**PROOF :** Join BE

We know that median divides the triangle into two triangles of equal areas ,

= AD is the median of Triangle ABC

So, area ( ABD ) = area ( ACD ) = 1/2 area ( ABC ) ----------- ( 1 )

As E is the mid point , i.e : BE is the median of triangle ABD ,

similarly , area ( BED) = area ( AEB )

or , area ( BED) = 1/2 area ( ABD )

Now , putting the value of area ( ABD ) from (1 ) ,

= area ( BED)= 1/2 [ 1/2 area ( ABC ) ]

= area (BED) = 1/2 * 1/2 area ( ABC )

**= area ( BED ) = 1/4 area ( ABC)**