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Math Help - Heron's forumla

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    Heron's forumla

    Heron's forumla-untitled12.jpg
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  2. #2
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    Hello, MATNTRNG!

    This one is surprisingly easy . . .


    The Indian mathematician Brahmagupta (7th century) found that
    the area of a cyclic quadrilateral with sides a,b,c,d is given by:

    . . A \;=\;\sqrt{(p-a)(p-b)(p-c)(p-d)}\;\text{ where }p = \frac{1}{2}(a+b+c+d)

    Show that Heron's Formula for the area of a triangle with sides a,b,c\!:
    . . . A \;=\;\sqrt{p(p-a)(p-b)(p-c)}\:\text{ where }p \:=\:\frac{1}{2}(a+b+c)
    follows from Brahmagupta's result.

    \text{Let }\,d = 0.

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