Final answer:
Polygon B's area is 16 times larger than Polygon A's area if it is a scaled copy with a scale factor of 4, because areas of similar figures are related by the square of the scale factor.
Step-by-step explanation:
When comparing the areas of two similar polygons, if Polygon B is a scaled copy of Polygon A with a scale factor of 4, then Polygon B's area is not just four times larger, but is in fact the square of the scale factor times bigger. This means that Polygon B's area is 42 or 16 times larger than the area of Polygon A.
Let's say we have a practical example where Marta has a square with a side length of 4 inches, and she creates a similar square with side lengths twice as long. The larger square would have a side length of 8 inches. To find the area, we calculate Area = side x side. For the original square, the area is 4 inches x 4 inches = 16 square inches. For the larger square, the area is 8 inches x 8 inches = 64 square inches. The larger square is therefore exactly 4 times longer on each side, but its area is 42, or 16 times greater than the smaller square.