Answer:
Suppose that we have two similar figures.
Then if a given side of one of the figures has a measure M, the correspondent side in the other figure has a measure M' = k*M
Where k is the scale factor.
Then if the perimeter of the first figure is P, the perimeter of the other figure will be P' = k*P
And if the area of the first figure is A, then the area of the other figure will be:
A' = k^2*A
Then the quotient between the perimeters is:
P'/P = k
And the ratio between the areas is
A'/A = k^2
So what we need to do, is find the value k.
In the image, we can see that the base of the larger figure is 30 yd, and the base of the smaller figure is 12 yd.
If we define the smaller figure as the original one, then we will have:
M = 12 yd
M' = 30 yd
M' = 30yd = k*12yd = k*M
Solving for k we get:
k = 30yd/12yd = 2.5
Then the ratio between the perimeters is:
P'/P = k = 2.5
And the ratio of the area of the larger figure (A') to the smaller figure (A) is:
A'/A = k^2 = (2.5)^2 = 6.25