Is calculators allowed? Cuz im just gonna use it.
Add all the vertical and horizontal lines in pattern 1 first. (its 7)
The diagonal lines are sqrt(2) cm long use pythagoream theorem. There are 6 of them
so pattern 1 is
do the same thing for pattern 2.
pattern 2 is 12 * sqrt(2) + 1
the ratio is \(\frac{6*\sqrt{2}+7}{12*\sqrt{2}+1}\)
now use calc