
#1
Oct1908, 10:06 PM

HW Helper
P: 6,214

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 xcoordinate 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 xcoordinate 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 ycoordinate 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
Oct1908, 11:04 PM

Sci Advisor
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P: 25,175

I think everyone's latex is failing tonight. Must have to do with the server migration. Let's just try this again later.




#3
Oct2008, 06:45 AM

Math
Emeritus
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PF Gold
P: 38,898

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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