Is it possible to draw a rectangle with the same area but smaller perimeters

Yes it is possible.

let's take a rectangle with 2 sides of 8 and 2 sides of 4

the area would be 32

and the perimeter would be 24

now, let's take another rectangle with 2 sides of 16 and 2 sides of 2

the area would be 32

and the perimeter would be 36

the areas are the same, but the perimeters are different.

therefore, it is possible.