Short Answer 
The area of a square is calculated using the formula (A = s^2), where (s) is the side length. For squares A and B, if square A has a side length of (166s) and square B has (s), the area ratio (k) of square A to square B is (k = 166^2), which equals (27556).
Step 1: Understand Square Area Formula
The area of a square is calculated by squaring its side length. Thus, for any square with side length (s), the area (A) can be expressed as:
- Area (A = s^2)
This formula is fundamental in determining the relationship between the areas of different squares based on their side lengths.
Step 2: Calculate the Area of Square A and Square B
If we denote the side length of square B as (s), then the side length of square A is (166s). The areas of both squares can be calculated as follows:
- Area of Square A = ((166s)^2 = 166^2 cdot s^2)
- Area of Square B = (s^2)
This simplifies our calculations by showing that the area ratio depends solely on (166^2).
Step 3: Determine the Ratio of Areas
To find the ratio (k) of the area of square A to the area of square B, you can use the areas calculated in the previous step:
- Ratio (k = frac{Area , of , Square , A}{Area , of , Square , B} = frac{166^2 cdot s^2}{s^2})
This results in (k = 166^2), which equals (27556). Thus, the ratio of the areas indicates how much larger square A is compared to square B.