Centroid of trapezoidal

The centroid of the trapezoidal with its one face perpendicular is given be $$ X=-1/3* {(-2b^2-2*a*b+a^2)/(a+b)}$$ $$Y=1/3 *h* (b+2*a)/(a+b)$$ Where a, b, h and origin is as shown in the figure below. Similarly, the centroid of any trapezoidal that does not have perpendicular face is given by $$x= 1/3*(3a*b+3*b*c+b^2+6*a*c+3*a^2+2*c^2)/(b+2a+c)$$ $$y=1/3* h* (b+3*a+c)/(b+2*a+c)$$ Where a, b…