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I need help with this finding a centroid of a triangle

  1. Oct 19, 2008 #1

    rock.freak667

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    Homework Helper

    1. The problem statement, all variables and given/known data

    Well I just need to understand how to find the centroid of a triangle, I know it's 2/3 from the vertex, but I need to know how finding it is done.


    2. Relevant equations

    [tex]\overline{x}= \frac{\int x dA}{\int dA}[/tex]

    [tex]\overline{y}=\frac{\int y dA}{\int dA}[/tex]


    3. The attempt at a solution

    Firstly I drew a triangle using the equation y=hx/b.



    Then I considered a small rectangular element, whose height is and width is [itex]\delta x[/itex].

    the area of this element is

    The Area of this small element is [itex]\delta A=y \delta x[/itex]

    Now the sum of all the infinitesmal areas is given by

    [tex]dA=\sum_{x=0}^{x=b} y \delta x[/tex]

    as [itex]\delta x \rightarrow 0[/itex]

    [tex]\int dA=\int_0 ^b y dx[/tex]
    1. The problem statement, all variables and given/known data

    Well I just need to understand how to find the centroid of a triangle, I know it's 2/3 from the vertex, but I need to know how finding it is done.


    2. Relevant equations

    [tex]\overline{x}= \frac{\int x dA}{\int dA}[/tex]

    [tex]\overline{y}=\frac{\int y dA}{\int dA}[/tex]


    3. The attempt at a solution

    Firstly I drew a triangle using the equation y=hx/b.



    Then I considered a small rectangular element, whose height is and width is [itex]\delta x[/itex].

    the area of this element is

    The Area of this small element is [itex]\delta A=y \delta x[/itex]

    Now the sum of all the infinitesmal areas is given by

    [tex]dA=\sum_{x=0} ^{x=b} y \delta x[/tex]

    as [itex]\delta x \rightarrow 0[/itex]

    [tex]\int dA=\int_0 ^b y dx[/tex]

    So the x-coordinate of the centroid is

    [tex]\overline{x}=\frac{\int_0 ^b \frac{h}{b}x^2}{\int_0 ^b \frac{h}{b}x}[/tex]
    So the x-coordinate of the centroid is

    [tex]\overline{x}=\frac{\int_0 ^b \frac{h}{b}x^2}{\int_0 ^b \frac{h}{b}x}[/tex]

    This is correct so far I assume, but what I do not understand is how to get the y-coordinate which should be the same answer.

    EDIT: If my latex is wrong, I will type it over, so far the preview is only showing latex which I have typed for previous questions and not what I actually typed in the post, yet when I post the message it says my latex code is invalid.
     
  2. jcsd
  3. Oct 19, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    I think everyone's latex is failing tonight. Must have to do with the server migration. Let's just try this again later.
     
  4. Oct 20, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The centroid of a triangle is simply the average of its three points. I searched through the code for your LaTex but I could find nowhere that you actually state what triangle you are talking about!
     
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