Number the parts:  

Part 1 rectangle: $b$ = 6 cm, $h$ = 4 cm.

Part 2 semicircle:  $r_o$ = 2 cm.

Part 3 circular hole: $r_i$ = 1.333 cm.

Calculate the areas:

$\begin{align} A_1 &= b h & A_2 &=  \tfrac{1}{2}\pi r_o^2 &A_3 &= \pi r_i^2&A&=A_1 +A_2 - A_3\\&=\var{display(A1)} &&=\var{display(A2)} &&=\var{display(A3)}&&=\var{display(A)}\\&&\end{align}$

Calculate the moment of inertia with respect to the x-axis.

$\begin{align} \\{I_1}_x &= \tfrac{1}{3} b h^3 \\&=  \tfrac{1}{3}( \var{b})(\var{h})^3 \\&= \var{display(Ix1)} \\\\{I_x}_2 &= [\bar{I} + A  d^2]_2\\  &= 0.1098 r_o^4 + \left(\frac{\pi r_o^2}{2}\right) \left(h + \frac{4 r_o}{3 \pi}\right)^2\\&= \var{display(Ibarx2)} + (\var{display(A2)}) (\var{display(d2)})^2\\&=\var{display(Ix2)} \\\\ {I_x}_3 &= [\bar{I} + A  d^2]_3 \\  &= \frac{\pi r_i^4}{4}  + \left(\pi r_i^2\right) \left(h \right)^2\\&= \var{display(Ibarx3)} + (\var{display(A3)}) (\var{display(h)})^2\\&=\var{display(Ix3)}\\\\I_x &= {I_x}_1+{I_x}_2-{I_x}_3\\&=\var{display(Ix1)}+\var{display(Ix2)}-\var{display(Ix3)}\\&=\var{display(Ix)}\end{align}$

Calculate the moment of inertia with respect to the y-axis.

$\begin{align} \\{I_y}_1 &= \tfrac{1}{3} h b^3 \\&= \tfrac{1}{3}( \var{h})(\var{b})^3 \\&= \var{display(Iy1)} \\\\{I_y}_2 &= [\bar{I} + A d^2]_2\\ &= \frac{\pi r_o^4}{8} + \left(\frac{\pi r_o^2}{2}\right) \left(\frac{b}{2}\right)^2\\&= \var{display(Ibary2)} + (\var{display(A2)}) (\var{display(b/2)})^2\\&=\var{display(Iy2)} \\\\ {I_y}_3 &= [\bar{I} + A d^2]_3 \\ &= \frac{\pi r_i^4}{4} + \left(\pi r_i^2\right) \left(\frac{b}{2} \right)^2\\&= \var{display(Ibary3)} + (\var{display(A3)}) (\var{display(b/2)})^2\\&=\var{display(Iy3)}\\\\I_y &= {I_y}_1+{I_y}_2-{I_y}_3\\&=\var{display(Iy1)}+\var{display(Iy2)}-\var{display(Iy3)}\\&=\var{display(Iy)}\end{align}$

Calculate the radius of gyration with respect to the x- and y- axes.

$\begin{align}\\k_x &= \sqrt{\dfrac{I_x}{A}}&k_y &= \sqrt{\dfrac{I_y}{A}}\\ &= \sqrt{\dfrac{\var{display(Ix)}}{\var{display(A)}}}&&= \sqrt{\dfrac{\var{display(Iy)}}{\var{display(A)}}}\\ &= \var{display(kx)} &&=\var{display(ky)} \end{align}$