Perimeter/footprint and square meters

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I'mIf a room is 8x8 meter the perimeter will be 32m, and 64m2. If add 2m on two sides and subtract 2m on two sides the room will be 10x6m. The perimeter, and footprint, will be the same for both rooms but the square meters will be different, can someone please explain this? I must be missing some fundamental logic here...

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Perimeter is the length of the boudary of a region, but, area covers the whole region. Your figure makes a square and a rectangle, both of which will give different area. It's just a co-incidence that you get the same perimeter. Figures will clear your doubts.