Geometry

posted by SkatingDJ

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

  1. Reiny

    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

  2. SkatingDJ

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

  3. Reiny

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

  4. SkatingDJ

    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?

  5. Reiny

    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

  6. Raaayleeee

    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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