Explanation:
41.
the original area is the sum of usually multiple calculations. in each one there is the product of 2 side lengths the deciding factor.
this is the principle of every area calculation.
now, when there is a version of the same shape with a scale factor s, then that means that every side length of the new shape is the length of the corresponding original side times s.
like in our case s = 3.
in the area calculation we have now the same calculations, but each side length is multiplied by s (3). so, they all contain now products like
sideA×3 × sideB×3 = sideA × sideB × 3×3 =
= sideA × sideB × 9
with sideA and sideB being the corresponding sides of the original shape.
and so, we see, as every calculation as part of the total sum for the area grows by the factor 3² = 9, then also the total area grows by the factor 3² = 9.
the area of Z = 11×9 = 99 units².
42.
as already indicated in 41., scaled versions of the same object differ from each other only by the side lengths, so that there is exactly one scale factor s that is the same for all pairs of corresponding sides (or also other lengths like heights,...).
so, the original was A.
what factor do we have to multiply the sides of A with to get the sides of B ?
since the factor has to be the same for every side, we only need to do this for one pair of sides - like 33 and 11 :
33 × s = 11
s = 11/33 = 1/3
the scale factor from A to B is 1/3.