Apair of corresponding sides of two similar pentagons have lengths of 14 cm and 21 cm. what is the ratio of the areas of the two pentagons?

By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

area=(s^2)n / 4 tan(180/n)

Area1=(14^2)5 / 4 tan(180/5) = 337.21 cm^2
Area2=(21^2)5 / 4 tan(180/5) = 758.73 cm^2

Therefore, the ratio of the area would be:

 337.21 cm^2/758.73 cm^2 = 0.4444