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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

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

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