Q. 224.8( 9 Votes )

The given figure shows a pentagon ABCDE, EG, drawn parallel to DA, meets BA produced at G, and CF, drawn parallel to DB, meets AB produced at F.

Show that ar(pentagon ABCDE) = ar(∆DGF).


Answer :

Given : ABCDE is a pentagon EG is drawn parallel to DA which meets BA produced at G and CF is drawn parallel to DB which meets AB produced at F


To prove: area(pentagon ABCDE) = area(∆DGF)


Proof:


Consider quadrilateral ADEG. Here,


area(∆AED) = area(∆ADG) ------------- (1)


[since two triangles are on same base AD and lie between parallel line i.e, AD||EG]


Similarly now, Consider quadrilateral BDCF. Here,


area(∆BCD) = area(∆BDF) ---------------- (2)


[since two triangles are on same base AD and lie between parallel line i.e, AD||EG]


Adding Eq (1) and (2) we get


area(∆AED) + area(∆BCD) = area(∆ADG) + area(∆BDF) ------------------ (3)


Now add area(∆ABD) on both sides of Eq (3), we get


area(∆AED) + area(∆BCD) + area(∆ABD) = area(∆ADG) + area(∆BDF) + area(∆ABD)


area(pentagon ABCDE) = area(∆DGF)


Hence proved


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Area of TriangleChamp Quiz | Area of TriangleChamp Quiz | Area of Triangle53 mins
Quiz | Area and ParallelogramQuiz | Area and ParallelogramQuiz | Area and Parallelogram46 mins
Quiz | Surface Area & VolumesQuiz | Surface Area & VolumesQuiz | Surface Area & Volumes49 mins
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder52 mins
Quiz | MensurationQuiz | MensurationQuiz | Mensuration42 mins
Champ Quiz | Area of ParallelogramChamp Quiz | Area of ParallelogramChamp Quiz | Area of Parallelogram55 mins
Surface Area and Volume of ConeSurface Area and Volume of ConeSurface Area and Volume of Cone24 mins
10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume52 mins
Quiz | Surface Area and VolumesQuiz | Surface Area and VolumesQuiz | Surface Area and Volumes43 mins
Quiz | Surface Area and VolumesQuiz | Surface Area and VolumesQuiz | Surface Area and Volumes43 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