Answer:
Explanation:
Perimeter
Let the smaller figure have n sides
Then the perimeter of the smaller figure = n * s
The perimeter of the larger figure = n*s1
The ratio would be n*s / n*s1 = 6/11 because the ns cancel out.
Area
The area is much harder.
If the figure is a regular polygon (all sides equal and convex) then both the sides and the apothem are both in a 6 to 11 ratio.
The formula for the area of a regular polygon is
Area = (n * s * a)/2
The apothem is the length of the line from the center of polygon to the middle of one of the sides.
S_L = the length of the larger side
S_s = the lenght of the smaller side
A_L = the length of the larger apothem
A_s = the length of the smaller apothem
Area_s = (n * S_L * A_L)/2
Area_L = (n * S_s * A_s)/2
The 2 s will cancel out
The ns will cancel out
S_s / S_L = 6/11
A_s / A_L = 6/11
Area_s / Area_L = (6 / ll ) ^2
Area_ s / Area_L = 36/121