In the given figure, ABCD is a parallelogram. BC is produced to point X. Prove that :

area (△ ABX) = area (quad.ACXD)

Since, ABCD is a parallelogram.

∴ AD // BC (Opposite sides of parallelogram are parallel)

We know that,

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

△ ABC and △ ADC lie on same base AC and between same parallel lines AD and BC.

∴ Area of △ ABC = Area of △ ACD ……..(1)

△ ACX and △ CXD lie on same base CX and between same parallel lines AD and BX.

∴ Area of △ ACX = Area of △ CXD ……..(2)

From figure,

⇒ Area of △ ABX = Area of △ ABC + Area of △ ACX

⇒ Area of △ ABX = Area of △ ACD + Area of △ CXD [From equation (1) and (2)]

⇒ Area of △ ABX = Area of quadrilateral ACXD.

Hence, proved that area (△ ABX) = area (quad.ACXD).