Question

In triangleDEF; A, B and C are mid points of sides EF, DF and DE respectively. If area of triangleBAF =24cm square, find area of AFBC

Answer 1

DC = CE  .
DB = BF .
∴BC ║ EF ( By mid point theorem).
BC = 1/2 EF.
BC = AF.
Similarly AC║BF.
AC= BF.
∴AFBC is a Parallelogram. 
ar(ABC)= ar(ABF)  (∵diagnol of a parallelogram divides it into two.                                            congruent triangles).
ar(ABF) + ar(ABC)=ar (AFBC).
24 + 24 = ar(AFBC).
ar (AFBC) = 48 sq.cm.