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

User Kerwyn
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1 Answer

1 vote

Answer:

The of the pentagon is A=232.48cm²

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

User VinceFR
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5.9k points