That’s right, you cannot know unless you know the shape.
The minimum length would be if it were square — each side would be the square root of 12, or 2 X square root of 3.
So if each side was 2X sqrt 3, total would be 8X sqrt 3.
Sqrt of 3 is 1.732 -, so you’d need not less than 13.86 inches. Any other dimensions and its longer.
Actually you could do it with less if it were a circle, and a whole lot less if you gave one end a half twist, and sewed the opposing edges together like a moebius strip.