The similarity ratio of two similar polygons is 2 and 3 Compare the smaller polygon to the larger polygon Find the ratio of their areas?

Answer 1

The similarity ratio of the two polygons is given as 2:3, meaning that the sides of the smaller polygon are 2 units for every 3 units of the larger polygon. The ratio of their areas is the square of the ratio of their corresponding side lengths. Thus, the area ratio is ( (2^2):(3^2) = 4:9 ). Therefore, the ratio of the area of the smaller polygon to the area of the larger polygon is 4:9.

Answer 2

For two similar polygons, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. Given the similarity ratio of the smaller polygon to the larger polygon is 2:3, we calculate the area ratio as follows: ( \left(\frac{2}{3}\right)^2 = \frac{4}{9} ). Therefore, the ratio of the areas of the smaller polygon to the larger polygon is 4:9.