How to Find the Centroid of a Composite Shape?

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SUMMARY

The discussion focuses on calculating the centroid of a composite shape consisting of a rectangle and a right-angled triangle. The method involves determining the area and centroid of each individual shape, followed by using the formulae x̄ = (1/A) * ∫(x * dA) and ȳ = (1/A) * ∫(y * dA) to find the overall centroid. The solution requires multiplying each shape's centroid coordinates by their respective areas and dividing by the total area to obtain the final coordinates of the centroid.

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  • Understanding of composite shapes in geometry
  • Familiarity with integral calculus
  • Knowledge of centroid calculation methods
  • Ability to perform area calculations for basic geometric shapes
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  • Study the method for calculating centroids of irregular shapes
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  • Explore advanced centroid calculations for complex composite 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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