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GEOMETRY

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PLEASE HELP ME, I HAVE AN EXAM TOMORROW AND THIS THE ONLY QUESTION I HAVE. THE AREA OF A REGULAR HEXAGON IS 35 IN SQUARED. FIND THE LENGTH OF A SIDE. ROUND YOUR ANSWER TO THE NEAREST TENTH. I KNOW THE ANSWER IS 3.7 BUT I DON'T KNOW HOW TO GET IT!!

  • GEOMETRY -

    This site explains how to find the area of a regular hexagon.

    http://jwilson.coe.uga.edu/emat6680/parsons/mvp6690/unit/hexagon/hexagon.html

  • GEOMETRY -

    IM GOING TO CRY!!!!!!!!!!!!!!!!

  • GEOMETRY -

    But it doesn't say what the apothem or the perimeter is so HOW do I find the length of A side????? The website didn't help at all.

  • GEOMETRY -

    The area is made up of 6 equilateral triangles
    look at one of these. call each side x
    draw a perpendicular from a vertex to the base, call it h. Makes no difference which one, since all sides are the same
    We can find the height h by using Pythagoras

    ((1/2)x)^2 + h^2 = x^2
    (1/4)x^2 + h^2 = x^2
    h^2 = x^2 - (1/4)x^2 = (3/4)x^2
    h = √3x/2

    area of one triangle = (1/2)basexheight
    = (1/2)x(√3x/2)
    = (√3/4)x^2

    area of whole hexagon = 6(√3/4)x^2 = (3√3/2)x^2
    but this equals 35

    (3√3/2)x^2 = 35
    x^2 = 70/(3√3) = 13.4715
    x = 3.67035 , they rounded that off to 3.7

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