Tell whether the following statement is true or false:

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. Then area of pentagon ABCDE = area of triangle DGF.

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True

False

answer is A.

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Detailed Solution

Given a pentagon ABCDE.
The given figure shows a pentagon ABCDE . EG drawn parallel to DA meets BA producedat G and CF drawn parallel to DB meets AB produced at F .Prove that the area

The given figure shows a pentagon ABCDE . EG drawn parallel to DA meets BA producedat G and CF drawn parallel to DB meets AB produced at F .Prove that the area

As triangle DBC and DBF are on same base and between same parallels.
Area of triangle DBC = Area of triangle DBF
Also, triangle ADE and ADG are on same base and between same parallels.
Area of triangle ADE = Area of triangle ADG
Adding both area and area of triangle ABD both sides,
Area of triangle DBC + Area of triangle ADE + Area of triangle ABD = Area of triangle DBF + Area of triangle ADG + Area of triangle ABD
Area of pentagon ABCDE = area of triangle DGF
Given statement is true.
Hence, option 1 is correct.

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