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Math Help - Trig Word Problem

  1. #1
    Junior Member casey_k's Avatar
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    Post Trig Word Problem

    Please check it to see if it is correct. I got 200.67 from finding the area of the pentagon.
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  2. #2
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    25 is not the height of each triangular face ... it is the vertical height of the pyramid.

    the slant height of each face is s = \sqrt{a^2 + 25^2} , where a is the length of the pentagon's apothem.

    total surface area, A = area of base + area of faces

    A = \frac{1}{2}ap + \frac{1}{2}sp

    p is the pentagon's perimeter.
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  3. #3
    Junior Member casey_k's Avatar
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    apothem?

    How do u find the apothem?
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  4. #4
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    a = \frac{x}{2\tan\left(\frac{\pi}{n}\right)}

    a = apothem
    x = side length
    n = number of sides for the regular polygon
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  5. #5
    Junior Member casey_k's Avatar
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    The Answer: please check if it is correct

    Perimeter = 5(10.8) = 54

    Apothem = s(tan x)/2
    = 10.8 (tan 54)/2 = 7.4325

    s = sqrt 7.4325^2 + 25^2
    = 26.081

    A = 1/2 ap + 1/2 sp
    = 1/2 (7.4325)(54) + 1/2 (26.081)(54)
    = 904.8645
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