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Math Help - Area of hexagon

  1. #1
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    Post Area of hexagon

    A regular hexagon is inscribed in a circle with radius 11. Find the area of the hexagon.

    Any help is appreciated!
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  2. #2
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    Hello, live_laugh_luv27!

    A regular hexagon is inscribed in a circle with radius 11.
    Find the area of the hexagon.
    Make a sketch.
    We find that the hexagon is made up of six equilateral triangles of side 11.

    The area of an equilateral triangle of side x is: . A \:=\:\tfrac{\sqrt{3}}{4}x^2

    With side 11, the area is: . \tfrac{\sqrt{3}}{4}(11^2) \:=\:\tfrac{121\sqrt{3}}{4}


    The area of the hexagon is: . 6 \times\tfrac{121\sqrt{3}}{4} \;=\;\frac{363\sqrt{3}}{2}

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, live_laugh_luv27!

    Make a sketch.
    We find that the hexagon is made up of six equilateral triangles of side 11.

    The area of an equilateral triangle of side x is: . A \:=\:\tfrac{\sqrt{3}}{4}x^2

    With side 11, the area is: . \tfrac{\sqrt{3}}{4}(11^2) \:=\:\tfrac{121\sqrt{3}}{4}


    The area of the hexagon is: . 6 \times\tfrac{121\sqrt{3}}{4} \;=\;\frac{363\sqrt{3}}{2}
    Thanks for taking the time to explain that to me..I really appreciate your help
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