CBSE Class 9 Answered
D and E are mid points of BC and AC.
DE||AB and DE = (Mid-point Theorem)
Similarly, E and F are mid points of AC and AB.
EF||BC and EF =
In quadrilateral BDEF, DE||BF and FE||BD
BDEF is a parallelogram
Similarly, DCEF and AFDE are parallelograms.
We know that diagonal of a parallelogram divides it into two triangles of equal area.
Area (BFD) = Area (DEF) (For parallelogram BDEF)
Area (CDE) = Area (DEF) (For parallelogram DCEF)
Area (AFE) = Area (DEF) (For parallelogram AFDE)
Area (AFE) = Area (BFD) = Area (CDE) = Area (DEF)
Also,
Area (AFE) + Area (BDF) + Area (CDE) + Area (DEF) = Area (ABC)
Area (DEF) + Area (DEF) + Area (DEF) + Area (DEF) = Area (ABC)
4 Area (DEF) = Area (ABC)
Area (DEF) = Area (ABC)