Consider the picture below. Both rectangles have an area of 36 square units. However, they have different perimeters. Why? Look at the top rectangle. How many square units do NOT touch the border of the rectangle? Only 10. These 10, do not impact the perimeter at all. Now, consider the bottom rectangle. How many squares in it do NOT touch the border (thus impacting the perimeter)? In this case, 16. Area will take into account all 36 of the square units no matter how you arrange them. However, perimeter will only be impacted by those squares that touch the sides of the rectangle (or any shape). Thus, you can have a fixed area but a changing perimeter. And, as Biff suggest, think about a very skinny rectangle, for example a 1 by 36 rectangle. In that case, it still has an area of 36, but all 36 of the rectangles touch the sides of the shape and thus are part of the perimeter.

https://imgur.com/a/OEVwZ6d