The area of a Koch snowflake is finite, but the perimeter is infinite.
The perimeter is a simple curve. Ok you construct the snowflake with traingles, ie straight lines, but one can never construct a perfect Koch snowflake because we can never replicate the fractal detail. Same with circles... we're essentially constructing a circle with a very large number of very small straight lines. One can never construct a perfect circle... find me a circle, and a good enough magnifying glass, and I'll prove it's not a circle. Eventually, at a small enough scale, the curvature will be broken.

We know a circle's circumference is directly proportional to its radius... so if the radius is finite, then so is the circumference. What makes the snowflake different? I'm going to confidently propose that the perimeter of a Koch snowflake is directly proportional to its radius (probably at a ratio related to pi), which therefore makes it very much finite.