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8 April, 17:46

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

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  1. 8 April, 19:41
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    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
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