Perimeter: ##34.76852## (to the limit of my calculator)

Let ##a## be the length of the side opposite the ##45^@## angle

and ##b## the length of the side opposite the ##105^@## angle.

tells us

##color(white)(XXX)8/sin(30^@)=a/sin(45^@)=b/sin(105^@)##

##sin(30^@)=0.5##

##sin(45^@)=0.707107## (approx.)

##sin(105^@)=0.965926## (approx.)

##8/sin(30^@)=16##

##a=16xxsin(45^@)=11.31371##

##b=16xxsin(105^@)=15.45481##

##Perimeter = 8 + a + b##

##color(white)(XXXXX)=34.76852##