Geometry

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Find the area of a hexagon with the indicated apothem:

6 sqr root 3

108 sqr root 3 in.^2
432 sqr root 3 in.^2
96 sqr root 3 in.^2
216 sqr root 3 in.^2

Last question, don't know. Please help? Thanks

  • Geometry -

    Area = 1/2 x perimeter x apothem
    = 1/2 (6s)(6√3)

    once you tell me what the side (s) of the hexagon is, we an finish the question

  • Geometry -

    They don't tell you the sides, the apothem is all they give you.

  • Geometry -

    So, I guess we can't find the area, since we need the side

  • Geometry -

    Hm, I mean, there has to be a way to figure the side out with just the apothem. Problem is that I'm not good with formulas or square roots.
    First off, what is the apothem? What is 6 square root 3?

  • Geometry -

    ok, ok

    I stand corrected, there is a way, we have an angle.
    The apothem is the distance from the centre to the midpoint of a side

    Let's look at one of the triangles of the hexagon.
    It has a central angle of 60
    so in a right-angled triangle formed by the apothem and half the base, I'll call it x
    x/6√3 = tan 30
    x = 6√3tan30
    base = 12√3tan30= 12

    area = Area = 1/2 x perimeter x apothem
    = (1/2)(72)(6√3)
    = 216√3 units^2

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