I need help with this finding a centroid of a triangle

  1. rock.freak667

    rock.freak667 6,228
    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. Dick

    Dick 25,810
    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. HallsofIvy

    HallsofIvy 40,367
    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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