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The minimum perimeter of a polyomino is the perimeter of the most square shape that can be formed. If the area can't form a perfect square, the minimum is formed by wrapping the additional units in a spiral around the smallest square or rectangle.

Since 25 happens to be a perfect square (the square root is 5), the perimeter would be 2(5+5)=20. If the area were between 26 and 30 that would add two additional sides which would be 20+2. After 30 the units would wrap to a new side of the 5x6 arrangement (still a perimeter of 22) yielding a new perimeter of 22+2 or 24, which would persist until it exceeds 6x6, and so on.

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Q: What is the minimum perimeter of a polyomino with an area of 25?
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