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Math Help - Help with hexagon area question...

  1. #1
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    Help with hexagon area question...

    A regular hexagon has side 2 meters.
    A) Find the area of the hexagon
    B) Find the area of the circumscribed circle
    I'm pretty sure for B, I just use the height of the triangle inside the hexagon as the radius and solve.
    But not sure how to get A... I know I'm supposed to split the hexagon into 6 triangles and find the area of each of those triangles, but how do I find the height?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    a) Make a sketch. The hexagon is made up of 6 similar triangles, with the same base length of 2 metres. If you know any angle in the triangle, you can work out the height of the triangle, thus the area of all the triangles.

    A regular hexagon has 6 equal sides, hence, if you put a centre in the hexagon, each of the 6 triangles will have an angle of 360/6.

    From this, use trigonometric ratios, tan for instance to find the height.

    b) Use the height of one triangle to find the slant length (or the hypotenuse of the half triangle), the latter is the radius of the circle then find its area.

    EDIT: Mis-interpreted the definition of 'circumscribed'
    Last edited by Unknown008; November 19th 2010 at 01:02 AM.
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  3. #3
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    Further you can divide those 6 equilateral triangles into 12 right triangles with one leg of length 1/2 having angles of 60 and 30 degrees.
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  4. #4
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    Please note that an inscribed circle is one that fits completely inside the hexagon, while a circumscribed circle is one that fits completely outside (around) the hexagon. So the radius for your problem will be from the center to one of the vertices of the hexagon.
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