# I need help with this finding a centroid of a triangle

by rock.freak667
Tags: centroid, triangle
 HW Helper P: 6,202 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 $$\overline{x}= \frac{\int x dA}{\int dA}$$ $$\overline{y}=\frac{\int y dA}{\int dA}$$ 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 $\delta x$. the area of this element is The Area of this small element is $\delta A=y \delta x$ Now the sum of all the infinitesmal areas is given by $$dA=\sum_{x=0}^{x=b} y \delta x$$ as $\delta x \rightarrow 0$ $$\int dA=\int_0 ^b y dx$$ 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 $$\overline{x}= \frac{\int x dA}{\int dA}$$ $$\overline{y}=\frac{\int y dA}{\int dA}$$ 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 $\delta x$. the area of this element is The Area of this small element is $\delta A=y \delta x$ Now the sum of all the infinitesmal areas is given by $$dA=\sum_{x=0} ^{x=b} y \delta x$$ as $\delta x \rightarrow 0$ $$\int dA=\int_0 ^b y dx$$ So the x-coordinate of the centroid is $$\overline{x}=\frac{\int_0 ^b \frac{h}{b}x^2}{\int_0 ^b \frac{h}{b}x}$$ So the x-coordinate of the centroid is $$\overline{x}=\frac{\int_0 ^b \frac{h}{b}x^2}{\int_0 ^b \frac{h}{b}x}$$ 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.