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Math Help - Pythagorean Theorem?

  1. #1
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    Pythagorean Theorem?

    How can I use algebra to show that the area of an equilateral triangle of side length S, is given by:

    Area of the triangle(s)=(S^2)(Sqr root 3)
    ______________
    4

    Not sure how to begin, thanks very much
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  2. #2
    MHF Contributor
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    Quote Originally Posted by captaintoast87 View Post
    How can I use algebra to show that the area of an equilateral triangle of side length S, is given by:

    Area of the triangle(s)=(S^2)(Sqr root 3)
    ______________
    4

    Not sure how to begin, thanks very much
    HI

    Draw a triangle , call it \triangle ABC

    O is the midpoint of BC . AO is the height of the altitude of the triangle .

    AO=\sqrt{s^2-(\frac{s}{2})^2}

    =\frac{s\sqrt{3}}{2}

    Area =\frac{s\sqrt{3}}{2}\cdot s

     <br />
=\frac{s^2\sqrt{3}}{2}<br />
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