Final answer:
The ratio of the areas of two similar 6-sided polygons, where the side of the larger is 5 times the smaller, is the square of the scale factor, which is 25:1.
Step-by-step explanation:
The question asks for the ratio of the area of the larger polygon to the area of the smaller polygon, given that two 6-sided polygons are similar and a side of the larger polygon is 5 times as long as the corresponding side of the smaller polygon.
Since the two polygons are similar, the ratio of any one dimensional measurements, such as side lengths, will be the same for all corresponding one dimensional measurements. Given the scale factor for the side lengths is 5, this means that any side of the larger polygon is 5 times longer than that of the smaller polygon.
When comparing the areas of similar figures, the ratio of the areas is equal to the square of the scale factor. Therefore, the ratio of the area of the larger polygon to the area of the smaller polygon is:
52 : 12 = 25 : 1
The correct answer to the question is D. 25:1.