Q. 84.7( 20 Votes )

In the figure, AB

Answer :

i) Given AC || BF


Distance between two parallel lines is constant therefore if we consider AC as common base of ΔABC and ΔFAC then perpendicular distance between lines AC and BF will be same i.e height of triangles ΔABC and ΔFAC will be same


As ΔABC and ΔFAC are triangles with same base and equal height


area(ΔABC) = area(ΔFAC)


ii) since area(ΔABC) = area(ΔFAC)


add area(ACDE) to both sides


area(ΔABC) + area(ACDE) = area(ΔFAC) + area(ACDE) …(i)


From figure


area(ΔABC) + area(ACDE) = area(ABCDE) …(ii)


area(ΔFAC) + area(ACDE) = area(AFDE) …(iii)


using (ii) and (iii) in (i)


area(ABCDE) = area(AFDE)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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 :

In the figure, diAP- Mathematics

ABCD is a paralleAP- Mathematics

In the figure, XYAP- Mathematics

In a triangle ABCAP- Mathematics

In the figure, ∆AAP- Mathematics

P and Q are any tAP- Mathematics

Show that the diaAP- Mathematics

In the figure, ∆AAP- Mathematics

A farmer has a fiAP- Mathematics

In the figure, ifAP- Mathematics