(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: I need help with this finding a centroid of a triangle

**Physics Forums | Science Articles, Homework Help, Discussion**