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Locate the centroid of the shaded portion w.r.t to ox & oy axes (fig 7).
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The centroid always lies on the axis of symmetry ¯x=120mm

To find ¯y:

A1=Area of rectangle=120×240=28800 mm2

y1=(1202)=60mm

A2=Area of semicircle=π(90)22=1272304mm2

y2=1204(90)3π=81.8mm

¯y=A1y1+A2y2A1+A2=28800×60112723.4×81.82880012723.4=42.747mm

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