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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