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Math Help - What is the area of a regular pentagon if its apothem has a length of 4 feet and each

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    What is the area of a regular pentagon if its apothem has a length of 4 feet and each

    What is the area of a regular pentagon if its apothem has a length of 4 feet and each side has a length of 5.8 feet?

    A) 139.2 ft2
    B) 58 ft2
    C) 116 ft2
    D) 69.6 ft2
    E) 92.8 ft2
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    Quote Originally Posted by Leo34005 View Post
    What is the area of a regular pentagon if its apothem has a length of 4 feet and each side has a length of 5.8 feet?

    A) 139.2 ft2
    B) 58 ft2
    C) 116 ft2
    D) 69.6 ft2
    E) 92.8 ft2
    If the centre of the pentagon is joined to the vertices, the regular pentagon is divided into 5 isosceles triangles. The apothem of the pentagon is the altitude (height) of each isosceles triangle. The side of the pentagon is the length of the base of each isosceles triangle.

    Calculate the area of one of the isosceles triangles and then multiply by 5.


    Edit: The data given in the question is consistent, to one decimal place. If you've learned trigonometry you should attempt to show that, in fact, if the sidelength of the regular pentagon is 5.8' then the apothem is actually 3.9915' (correct to four decimal places).
    Last edited by mr fantastic; September 5th 2009 at 04:18 PM.
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    Is the answer 58?
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    Quote Originally Posted by Leo34005 View Post
    Is the answer 58?
    Yes.
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