Find centre of mass

Dear student 

Let divide the figure into four parts A, B, C and D as shown in figure

and their masses are m₁, m₂, m₃ and m₄ and centre of masses are $\left(x_1 y_1\right)$, $\left(x_2 y_2\right)$, $\left(x_3 y_3\right)$ and $\left(x_4 y_4\right)$.
Assume that the thickness and density are t and d and lower left corner of part A as the origin then
For part A:
mass m₁= length$\times$width$\times$thickness$\times$density
   $$\begin{gathered} m_1=10\times 2\times t\times d \\ \Rightarrow m_1=20td \end{gathered}$$
and x₁=1cm and y₁= 5cm

For part B:

$$\begin{gathered} m_2=4\times 2\times t\times d \\ \Rightarrow m_2=8td \end{gathered}$$
and ​x₂=4cm and y₂= 1cm

For part C:
$$\begin{gathered} m_3=4\times 2\times t\times d \\ \Rightarrow m_3=8td \end{gathered}$$
and x₃=4cm and y₃= 5cm

For part D :
$$\begin{gathered} m_4=4\times 2\times t\times d \\ \Rightarrow m_4=8td \end{gathered}$$
and x₄=4cm and y₄= 9cm

Let the centre of mass of the whole figure is $\left(X Y\right)$ then 
$$\begin{gathered} X=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4} \\ \Rightarrow X=\frac{20td\times 1+8td\times 4+8td\times 4+8td\times 4}{20td+8td+8td+8td} \\ \Rightarrow X=2.63 cm \\ and \\ \Rightarrow Y=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4}{m_1+m_2+m_3+m_4} \\ \Rightarrow Y=\frac{20td\times 5+8td\times 1+8td\times 5+8td\times 9}{20td+8td+8td+8td} \\ \Rightarrow Y=5cm \end{gathered}$$

Therefore the centre of mass of the given E shaped figure is (2.63cm, 5cm).