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Locate the centroid of the shaded position w.r to OX & OY axis (fig.)

enter image description here

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All the data can be seen from the figure itself

Since, the figure is symmetric, x coordinate can be directly given by observation. Which is 240/2.

Therefore, X=120mm

enter image description here

Y=Ay/A=687749/16083=120=42.8mm

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