Question
Tue January 29, 2013 By:

Prove that area of triangle GBC = area of quadrilateral AFGE.

Expert Reply
Wed January 30, 2013
Median divides the triangle into 2 triangles BEC and BEA of equal area

ar(BEC) = ar(BEA) ............... (1)

Triangles BFC and BEC have equal areas because they have same base BC and lie between same parallels BC and FE

ar(BFC) = ar(BEC) ............... (2)

From (1) and (2),

ar(BFC) = ar(BEA)

subtracting ar(FGB) on both sides, we get ar(AFGE) = ar(BGC)

Related Questions
Home Work Help