Geometry

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

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  1. 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

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    posted by Reiny
  2. They don't tell you the sides, the apothem is all they give you.

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

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    posted by Reiny
  4. 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?

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  5. 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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    posted by Reiny
  6. Unit 5: Area
    Lesson 4: Perimeters and Areas of Similar Figures
    Perimeters and Areas of Similar Figures Quiz
    1) A - 14.04cm^2
    2) A - 34cm^2
    3) A - 144.5cm^2
    4) D - 12cm
    5) A - 144 + 72squareroot3
    6) B - 15.9ft^2
    7) D - 72squareroot3
    8) B - 73.5squareroot3cm^2
    9) C - 5 : 4 and 25 : 16
    10) C - 3181m^2
    11) A - $81.25
    12) D - the area would not change
    13) D - 216squareroot3in^2
    100%

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  7. Raaayleeee is right

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  8. You are 100% correct! Thanks!!

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