How to Find the Centroid of a Composite Shape?

[Hybrid_Theory]

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?

 

[LawrenceC]

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)

 

[Hybrid_Theory]

Thank you.