If D, E and F are the mid points of BC, CA and AB respectively of the ΔABC then the ratio of area of the parallelogram DEFB and area of the trapezium CAFD is :
D and E are midpoints of BC and AC respectively. ∴ DE || BA ⇒ DE || BF, FE || BD DF is the diagonal of parallelogram BDEF. ∴ Area of ΔBDF = Area of ΔDEF Similarly DE is the diagonal of parallelogram DCEF. ∴ Area of ΔDCE = Area of ΔDEF ∴ ΔBDF = ΔDCE = ΔAFE = ΔDEF ∴ On adding 4 × ΔDEF = ΔABC Parallelogram BDEF = 2 × ΔDEF = × ΔABC Quadrilateral CAFD = ΔABC – ΔBDF = ΔABC – ΔBDF = × ΔABC ∴ Required ratio = × ΔABC : ΔABC = 2 : 3