It's not entirely clear what the full instructions are, and I wish your teacher posted a diagram of figures A and B. However, I think I know what your teacher is after.
I'm assuming this is pertaining to similar polygons.
The larger figure has a side length of 88 ft and corresponds to the smaller side length of 11 ft. This is a scale factor of 11/88 = 1/8 = 0.125
What it means is that we multiply each larger side length by 1/8 or 0.125 to get the smaller corresponding side length. In other words, 88*(1/8) = 11
Square this linear scale factor to get the area scale factor
(1/8)^2 = (0.125)^2 = 0.015625
This value of 0.015625 is the area scale factor. We multiply this by the area of figure A to get
4928*0.015625 = 77
This is how your teacher got 77 as the final answer for figure B.
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Admittedly this concept is a bit confusing at first.
Let's do another example.
Consider a 2 by 3 rectangle of area 2*3 = 6 square units.
Now apply a linear scale factor of 4 to quadruple each side. We get a 8 by 12 rectangle of area 8*12 = 96.
Notice the jump from 6 to 96 is "times 16" (since 96/6 = 16) and it's no coincidence that 16 is 4^2, i.e. the result of squaring the linear scale factor.
new area = (area scale factor)*(old area)
new area = 16*(old area)
new area = 16*6
new area = 96
This shows that 16 is the area scale factor.
