In ΔABC, a line segment DE is drawn through the centroid G, parallel to side BC. D lies on AB, and E lies on AC. What is the ratio of the area of the smaller ΔADE to the area of the trapezoid DECB?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4:5.
DE ∥ BC through centroid G.
AD/AB = 2/3
⇒ Area(ΔADE) : Area(ΔABC) = (2/3)2 = 4/9
Area of trapezoid DECB = 1 − 4/9 = 5/9
Area(ΔADE) : Trapezoid DECB = (4/9) : (5/9) = 4 : 5