Final answer:
To find the area of pentagon S, we can set up an equation using the ratios of the areas of R and S. Using this equation, we can solve for the area of S in terms of its side length.
Step-by-step explanation:
Pentagons R and S are similar. If the area of pentagon R is 13 cm2, we can find the ratio of the areas of R and S, which will translate to the ratio of their side lengths squared. Let's assume the side length of R is 5 cm, and the side length of S is x cm. Using the ratios of the areas, we can set up the equation:
52 / x2 = 13 / AS
where AS is the area of S. Cross multiplying and rearranging the equation, we can find:
AS = (x2 * 13) / 52
Substituting the given values:
AS = (x2 * 13) / 25