If D, E, F are mid-points of sides BC, AB and AC respectively of an equilateral triangle ABC, then ratio of the area of triangle DEF and DCF is?

1 : 2 1 : 1 2 : 1 1 : 4

1 : 1

As D, E and F are the mid points of the sides, therefore, as per mid point theorem, "The triangle made by joining the mid points divides the actual triangle in four equal parts. Hence,  area of triangle DEF : area of triangle DCF = 1 : 1