In the given figure, AD // BE // CF. Prove that :

area (△ AEC) = area (△ DBF)

We know that,

Area of triangles on the same base and between the same parallels lines are equal.

From figure,

△ BDE and △ ABE lie on same base BE and between same parallel lines AD and BE.

∴ Area of △ ABE = Area of △ BDE ………..(1)

△ BEC and △ BEF lie on same base BE and between same parallel lines CF and BE.

∴ Area of △ BEC = Area of △ BEF …………(2)

Adding equations (1) and (2), we get :

⇒ Area of △ ABE + Area of △ BEC = Area of △ BDE + Area of △ BEF

⇒ Area of △ AEC = Area of △ DBF.

Hence, proved that area (△ AEC) = area (△ DBF).