The A4 Paper Puzzle

A puzzle to work out the perimeter of a shape (NO SPOILERS!) complete with an introduction to hash functions. DO NOT put your answer tot he puzzle in the comments below. If you want to check your answer, repeatedly take the square-root five times and if the first six non-zero digits after the decimal point are 234477 (in numerical order) then you are correct. Or check your answer using the SHA-256 hash function: Watch James on Numberphile talk about √2 and A4: Watch me apologise for making fun of Imperial units: MATT PARKER: Stand-up Mathematician Website: Music by Howard Carter Design by Simon Wright