Question

A pair 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?

Answer 1

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