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geometry

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A regular hexagon has an area of 96sqrt3. What is the length of each side of the hexagon?

  • geometry -

    The area of a polygon of n sides with an apothem of a and side c is
    A=nac/2

    For a hexagon,
    n=6, apothem=c*sqrt(3)/2
    so
    Area=6*c*(sqrt(3)/2)*c/2
    =3c²sqrt(3)

    In the given case,
    96sqrt(3) = 3c²sqrt(3)
    Solve for c (length of side).

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