8. Each deformation internal angle is (8-2) × 180 ÷ 8 = 135.

According to the definition of adjacent complementary angles, it is not difficult to find that △MGF, △ Ned, △HQA and △BCR are isosceles right triangles.

Quadrilateral MQRN is a rectangle.

∴MQ=RN,MN=QR

MN = MF+FE+EN =√2+6+5√2/2 = 6+7√2/2 = QR = QA+a b+BR = QA+7+2√2

QA=3√2-1, then HA=6-√2.

Similarly, Hg = 3+2/2.

So the perimeter of the octagon = AB+BC+CD+DE+EF+FG+GH+HA = 7+4+2+5+6+2+3+√ 2/2+6-√ 2.

=35-√2/2