In triangle ABC, DE is drawn parallel to BC with D on AB and E on AC, such that AD = 4 and DB = 6. If the area of triangle ADE is 20 sq. units, find…

Since DE ∥ BC, triangle ADE is similar to triangle ABC, with AD/AB = 4/10 = 2/5. The ratio of areas of similar triangles equals the square of the ratio of corresponding sides: Area(ADE)/Area(ABC) = (2/5)² = 4/25. So Area(ABC) = 20×25/4 = 125 sq. units. The trapezium DBCE is the remaining region: Area(DBCE) = 125 − 20 = 105 sq. units.