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Thread: Geometry - apothems regular polygon area stuff

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    Geometry - apothems regular polygon area stuff

    Can someone explain to me how to find the length of a side and the apothem of a polygon (hexagon for instance), given the area of the hexagon, (841.8units2)?

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    bamag's Avatar
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    Apothems are lines from the center of the polygon to a side such that it creates a right angle. For example:

    Regular polygons can be cut up into a bunch of right triangles.
    The pentagon pictured above can be cut into 6 triangles. Let a = length of apothem and s = length of side.
    Each triangle has area (1/2)(a)(s)=(as/2). Since there's 5 triangles, you multiply that by 5 to get (5as)/2.
    In general, the area would be (as/2)(n) with n being the number of sides.
    I think that's how it works, lemme go google to verify myself xD
    Last edited by bamag; 02-04-2012 at 06:27 PM.

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    Quote Originally Posted by bamag View Post
    Apothems are lines from the center of the polygon to a side such that it creates a right angle. For example:

    Regular polygons can be cut up into a bunch of right triangles.
    The pentagon pictured above can be cut into 12 right triangles. Let a = length of apothem and s = length of side.
    Each right triangle has area (1/2)(a)(s/2)=(as/4). Since there's 10 triangles, you multiply that by 10 to get (5as)/2.
    In general, the area would be (as/4)(2n) with n being the number of sides.
    I think that's how it works, lemme go google to verify myself xD
    im looking to find the measure of the apothem and side....with a given area...not trying to find the area

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    My bad.

    where
    A is the length of the apothem (inradius)
    N is the number of sides

    841.8=A^2(6)tan30=6*sqrt3*A^2
    A^2 = 841.8/(6*sqrt3)= around 81
    A=9 units

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    kidchaor (02-04-2012)

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