Q. 203.7( 3 Votes )

The given figure shows a pentagon ABCDE in which 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: EG||DA, CF||DB


Here, in Quadrilateral ADEG


Area (Δ AED) = Area (Δ ADG) –1


In Quadrilateral CFBD


Area (Δ CBD) = Area (Δ BCF) –2


Add –1 and –2


Area (Δ AED) + Area (Δ CBD) = Area (Δ ADG) + Area (Δ BCF) –3


Add Area (Δ ABD) to –3


Area (Δ AED) + Area (Δ CBD) + Area (Δ ABD) = Area (Δ ADG) + Area (Δ BCF) + Area (Δ ABD)


Area (pentagon ABCDE) = Area (∆DGF)


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