If the ratio of sides between two similar figures is 6/11, then what would be the area and perimeter ratios?

Step-by-step 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

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: