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What is the area of a regular hexagon with a radius of 7square root 3?

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What is the area of a regular hexagon with a radius of 7square root 3?

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  1. A = 1/2ap, where a is the apothem (radius) and p is the perimeter

    The apothem of a regular hexagon is always 1/2s*sqrt3, where s is one of the side lengths, so a side length of this hexagon is 14. Thus the perimeter of the hexagon is 14*6 = 84.

    A = 1/2ap

    1/2(7sqrt3)(84)

    42(7sqrt3)

    294sqrt3 square units <===ANSWER


  2. What is the area of a regular hexagon with a radius of 7square root 3?

    cece_121...here it is:

    http://www.flickr.com/photos/27678773@N0...

    In the Hexagon the central angle = 60°

    Hexagon has 6 sides

    360° ÷ 6 = 60°

    The Area of the sector with central Angle = 60°

    From the Diagram

    Cos 60° =  AC/AO

    AC = AO  Cos 60°

    AC = 7√3 (0.5)

    Area Equilateral Triangle = ½ Base x Height

    Area Equilateral Triangle = ½ AC x OC

    Sin 60° = OC /OA

    OC =  OA Sin 60°

    OC =  7√3 (0.866)

    Area Equilateral Triangle = ½ AC x OC

    Area Equilateral Triangle = ½ (7√3 )( 0. 5) x 7√3 (0.866)

    Area Equilateral Triangle =  (7√3 x 7√3 (0.866)(0.25)

    Area Equilateral Triangle = 49(3) x (0.866) (0.25)

    Area Equilateral Triangle =  31. 83

    Area of the Hexagon = Area of the Triangle x  6

    Area of the Hexagon = 31. 83  x  6

    ======================================...

    Ans::Area of the Hexagon = 190. 95

    ======================================...

    Hope this helps

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