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Math Help - Trigonometry and area

  1. #1
    Junior Member
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    Trigonometry and area

    I need help with a few problems.

    I need help finding the area of a regular hexagon with an apothem of 19mm.
    Also I need help with finding the area of a octagon with a radius of 20in.

    Can someone also double check if I did these ratio right?

    A similar pair of triangles the small triangle has a area of 12 cm and the large has an area of 48 cm.
    Ratio of areas = 1:4
    Scale factor = 4
    Ratio of perimeter = 1:4

    Did I do that one right?
    Thanks for your help.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Jubbly View Post
    I need help with a few problems.

    I need help finding the area of a regular hexagon with an apothem of 19mm.
    Also I need help with finding the area of a octagon with a radius of 20in.

    Can someone also double check if I did these ratio right?

    A similar pair of triangles the small triangle has a area of 12 cm and the large has an area of 48 cm.
    Ratio of areas = 1:4
    Scale factor = 4 in terms of two-dimensional areas
    Ratio of perimeter = 1:4 perimeter is one-dimensional

    Did I do that one right?
    Thanks for your help.
    Hi Jubbly,

    As area is 0.5(base)(height)

    Quadrupled area corresponds to 0.5[(2)base][2(height] for similar triangles.

    Therefore the ratio of perimeters, corresponding to area ratio of 1:4, is 1:2

    see the attached sketch.
    Attached Thumbnails Attached Thumbnails Trigonometry and area-similar-triangles.jpg  
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