The centroid of shaded area can be obtained By taking whole rectangle of 110 X 90 then Subtracting a triangle of base 75 & height 90 & square of side 50 X 50 from it. Also at the end Adding quarter circle of radius 50 to it

Now, $X = (\sum A_i x_i)/( \sum A)= 367831.15/5988.49= 61.42 \\ Y = (\sum A_i y_i)/( \sum A)= 341224.66/5988.49= 56.98 $

Centroid of shaded region is $(61.42, 56.98)$ units