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Math Help - A generalized formula for finding the area of a regular polygon

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    A generalized formula for finding the area of a regular polygon

    Is this possible? Assume a polygon that has all equal angles and lengths
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    Quote Originally Posted by evankiefl View Post
    Is this possible? Assume a polygon that has all equal angles and lengths
    Sure!

    A regular polygon has "n" sides.
    Therefore it may be subdivided into "n" isosceles triangles, all meeting at the centre.

    The angle at the central apex of each triangle is 360/n degrees.

    Subtract that from 180 degrees and divide by 2 to get the other angles "A" of each isosceles triangle.
    Take half the length of a side of the polygon.
    Use TanA multiplied by half a side length squared to get a triangle area.

    "n" of these is the polygon area.
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    when you take TanA, is it of half of the isosceles triangle?
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    Quote Originally Posted by evankiefl View Post
    when you take TanA, is it of half of the isosceles triangle?
    Here is the situation....

    "x" is half the length of a side.
    "h" is the perpendicular height of each isosceles triangle.

    TanA=\frac{h}{x}\Rightarrow\ h=xTanA\Rightarrow\ xh=x^2TanA

    That is the area of each isosceles triangle
    (twice the area of the right-angled triangle as 2 of these form the isosceles triangle).

    Multiply by "n" for the polygon area.
    Attached Thumbnails Attached Thumbnails A generalized formula for finding the area of a regular polygon-polygon.jpg  
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