What is the area of a regular pentagon with an apothem of 8 centimeters

The of the pentagon is A=232.48cm²

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, a pentagon

Now given the apothem the area can be expressed as

A=a²n tan (180/n)

where

a = the length of the apothem (in radius)

n = the number of sides = 5 for pentagon

tan is the tangent function calculated in degrees

Substituting our given data we can solve for the area A

A = 8²*5 tan (180/5)

A = 64*5 tan 36

A = 320tan 36

A = 320*0.7265

A=232.48cm²