Question

In the given figure, AD // BE // CF.
Prove that area (ΔAEC) = area (ΔDBF)

Answer 1

We know that the area of triangles on the same base and between the same parallel lines are equal.

Consider ABED quadrilateral; AD || BE.
With the common base, BE and between AD and BE parallel lines, we have
Area of ΔABE = Area of ΔBDE

Similarly, in BEFC quadrilateral, BE || CF
With common base BC and between BE and CF parallel lines, we have
Area of ΔBEC = Area of ΔBEF

Adding both equations, we have
Area of ΔABE + Area of ΔBEC = Area of ΔBEF + Area of ΔBDE
⇒ Area of AEC = Area of DBF

Hence Proved.