Consider the figure

Center of mass,

$\overline{)\begin{array}{rcl}\mathbf{C}\mathbf{.}\mathbf{M}\mathbf{}\mathbf{=}\mathbf{}\mathbf{[}\mathbf{X}& {\mathbf{=}}& \frac{{\mathbf{M}}_{\mathbf{a}}{\mathbf{X}}_{\mathbf{C}\mathbf{a}}\mathbf{+}{\mathbf{M}}_{\mathbf{b}}{\mathbf{X}}_{\mathbf{C}\mathbf{b}}}{{\mathbf{M}}_{\mathbf{a}}\mathbf{+}{\mathbf{M}}_{\mathbf{b}}}\mathbf{,}\mathbf{}\begin{array}{cl}\mathbf{Y}\mathbf{=}& \frac{{\mathbf{M}}_{\mathbf{a}}{\mathbf{Y}}_{\mathbf{C}\mathbf{a}}\mathbf{+}{\mathbf{M}}_{\mathbf{b}}{\mathbf{Y}}_{\mathbf{C}\mathbf{b}}}{{\mathbf{M}}_{\mathbf{a}}\mathbf{+}{\mathbf{M}}_{\mathbf{b}}}\end{array}\mathbf{]}\end{array}}$

M = Aσ

M_{a} = (16-8)(6)σ = (48 cm^{2})σ

M_{b} = (15)(8.0)σ = (120 cm^{2})σ

Calculate the center of mass of the object below. Assume the mass is uniformly distributed.