Answer:
16 cm
Step-by-step explanation:
"regular polygon" means all sides and angles are the same.
the sum of all exterior angles must be 360 degrees.
so, how often do 45 fit into 360 ?
2 times in 90, which in turn fit 4 times into 360, so 8 times.
the polygon has 8 corners and 8 sides.
each side is originally 10cm
so the original perimeter is 8×10 = 80 cm
now, every side is reduced to 1/5th of the original size, this also reduces the perimeter by the same factor.
=> perimeter = 80×(1/5) = 80/5 = 16 x cm
control :
applying the scaling factor of 1/5th to every side transforms every side from 10 cm to 2 cm.
we still have 8 sides.
perimeter = 8 × 2 = 16 cm
correct
