Q. 74.0( 2 Votes )

The points D and E are on the sides AB and AC of ΔABC respectively, such that DE || BC. If AB = 3 AD and the area of Δ ABC is 72 cm2, then find the area of the quadrilateral DBCE.

Answer :


Here,


In ΔADE and ΔABC


ADE = ABC by corresponding angles (DEBC)


DEA = BCA by corresponding angles (DEBC)


ΔAED ΔACB


Similarly,


ΔAGD ΔAFB (where AF BC)


AF = 3AG ( AB = 3AD which is given) ----(1)


Similarly,


BC = 3×DE ----(2)


{by (1) and (2)}



Area of ΔABC = 9 × Area of ΔADE


( Area of ΔABC = 72 cm2)


Area of ΔADE = 8 cm2


Area of DCEB = Area of ΔABC - Area of ΔADE


Area of DCEB = 72 – 8 = 64cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Some Interesting Proofs in GeometrySome Interesting Proofs in GeometrySome Interesting Proofs in Geometry36 mins
Section FormulaSection FormulaSection Formula30 mins
Previous Year RMO QuestionsPrevious Year RMO QuestionsPrevious Year RMO Questions43 mins
NCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in TrianglesKnow About Important Proofs in TrianglesKnow About Important Proofs in Triangles33 mins
Measuring distance by Distance formulaMeasuring distance by Distance formulaMeasuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE Questions29 mins
Smart Revision | Become a Master in Coordinate GeometrySmart Revision | Become a Master in Coordinate GeometrySmart Revision | Become a Master in Coordinate Geometry54 mins
Champ Quiz | Distance FormulaChamp Quiz | Distance FormulaChamp Quiz | Distance Formula30 mins
Set of Questions on Section FormulaSet of Questions on Section FormulaSet of Questions on Section Formula54 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :