Question

If D,E,F are respectively the mid points of the sides BC,CA,AB of a triangle ABC, then what is the ratio of the area of triangle DEF and area of triangle ABC?

Answer 1

hey
_________________

DEFB is a ||gm and diagonal of || divides into two ∆ of equal area

ar∆DBE = ar∆DFE

similarly , ar∆DEC=ar∆DFE
similarly, ar∆AFE=ar∆DFE

all the area of triangles are equal
so ar ∆ABC= ar∆DBE+ar∆DEC+ar∆AFE+ar∆DFE

we can write , 4×ar∆DFE=ar∆ABC
ar∆DFE=1/4ar∆ABC

hence ratio of ∆DFE is 4:1 to the ar∆ABC

hope helped
__________________

Answer 2

hey mate
refer to attachment