How to Find the Centroid of a Composite Shape?

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To find the centroid of a composite shape, first calculate the area and centroid of each individual component, such as the rectangle and the right-angled triangle. Next, multiply the centroid coordinates (xbar and ybar) of each shape by their respective areas. Finally, sum these products and divide by the total area of the composite shape to determine the overall centroid coordinates. The formulas xbar = (1/A) * integral(x * dA) and ybar = (1/A) * integral(y * dA) are essential for these calculations. This method ensures an accurate determination of the centroid for irregular shapes.
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Homework Statement


As part of a test I was given an irregular shape to find its centroid. It was a rectangle with a right angled triangle on its right side (I don't have a picture to upload for ye unfortunately).

Homework Equations


dA=y.dx
X(bar)=intrecal x.y.dx
Y(bar)=intrecal y^2/2.dy

The Attempt at a Solution


I worked out the area and centroid of the rectangle and triangle separately but didn't know how to find the overall centroid. How would you do this?
 
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Compute the centroid of each part, xbar and ybar. Compute the area of each. Multiply each centroid, xbar and ybar, by its respective area. Then divide by the total area to get the location of XBAR and YBAR.

By the way, xbar = (1/A)*integral (x*dA),
ybar = (1/A)*integral (y*dA)
 
Thank you.
 
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