Question

EFGH is a parallelogram with diagonal EG and FH meeting at a point X. show that ar (traingle EXF) =ar(traingle GXF)=ar(triangle HXG)

Answer 1

X is the mid point of both the diagonals[diagonals of a parallelogram bisect each other]
In tri. EFG
XF is the median
therefore ar (EXF)=ar (GXF)[since, median of a triangle divides the triangle into two triangles of equal area]
In tri. FGH
GX is the median
therefore ar (HXG)=ar (GXF) [since, median of a triangle divides the triangle into two triangles of equal area]

therefore ar (EXF)=ar (GXF)=ar (HXG)

{Hence proved}