Question -
Answer -
It is given that
XY || BC ⇒EY || BC
BE || AC ⇒BE || CY
Therefore, EBCY is aparallelogram.
It is given that
XY || BC ⇒XF || BC
FC || AB ⇒FC || XB
Therefore, BCFX is aparallelogram.
Parallelograms EBCY andBCFX are on the same base BC and between the same parallels BC and EF.
∴Area (EBCY) = Area (BCFX) … (1)
Consider parallelogramEBCY and ΔAEB
These lie on the same baseBE and are between the same parallels BE and AC.
∴Area (ΔABE) = 
Area (EBCY) … (2)
Also, parallelogram BCFX andΔACF are on the same base CF and between the same parallels CF and AB.
∴Area (ΔACF) = Area (BCFX) … (3)
From equations (1), (2),and (3), we obtain
Area(ΔABE) = Area (ΔACF)