Processing Polyomino Perimeter

For each square that you add to a polyomino, you are increasing the total perimeter by 4. Therefore, you want to surround squares, with others, hence removing this increase. This fits with the fact that, for a given area, the smallest perimeter is given by a square. $45^2 = 2025$ , so they will all fit inside a square this size. Note that despite $2018 = 45 \cdot 44 + 38$ , this doesn't change the perimeter from it being a full square, if they are all stacked from one side inwards. If you want to visualise this, picture an L shape which has the same perimeter as a rectangle. Therefore the answer is $\boxed{4 \cdot 45 = 180}$