Final answer:
The ratio of the areas of two similar polygons with corresponding sides in a ratio of 2:3 is the square of the scale factor, which is 4:9.
Step-by-step explanation:
The question asks for the ratio of the areas between two similar polygons with corresponding sides in a ratio of 2:3. When comparing the areas of similar figures, the ratio of the areas is the square of the scale factor. By squaring the given scale factor of the sides, which is 2:3, we obtain (22):(32)=4:9. Therefore, the ratio of the areas of the polygons is 4:9, which corresponds to option D.