CAN PERIMETER OF ABCD PARALLELOGRAM IS EQUAL OR GREATER OR LESS THAN PERIMETER OF ABFE RECTANGLE ON SAME BASE IF YES THAN GIVE SOME EXAMPLE OR ALSO PROVE

Consider the following diagram

 

 

Here ABCD is the parallelogram and ABFE is the rectangle.

 

AC and BD are the hypotenuse of the right triangles AEC and BFD respectively.

 

Thus, by Pythagoras Theorem, it is clear that the lengths AC and BD are greater than the lengths of AE and BF respectively.

 

Therefore, the perimeter of the parallelogram ABCD is greater than the perimeter of the rectangle ABFE.