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We have this relationship

NW / NO = NO / NS

NW / 6  =  6 / 8

NW =  36 / 8   =    9/2  =  4.5

So....using the Pythagorean Theorem

WO =  sqrt ( 6^2 + 4.5^2 )  =  sqrt (56.25)  = 7.5

So....the perimeter is

WO + NW + NS + SO =

7.5 + 4.5 + 8 + 10   =

12 + 8 + 10 =

30