Question

In the given figure, ABCD is a parallelogram; BC is produced to point X.
Prove that: area ( Δ ABX ) = area (`square`ACXD )

Answer 1

Given: ABCD is a parallelogram.
We know that
Area of ΔABC = Area of ΔACD
Consider ΔABX,
Area of ΔABX = Area of ΔABC + Area of ΔACX
We also know that the area of triangles on the same base and between the same parallel lines are equal.
Area of ΔACX = Area of ΔCXD
From the above equations, we can conclude that
Area of ΔABX = Area of ΔABC + Area of ΔACX
= Area of ΔACD+ Area of ΔCXD
= Area of ACXD Quadrilateral

Hence Proved.