Check the picture below.
so we can simply get the areas of the rectangular part, notice its top is inside the box, so we exclude that, and the area of a semi-cylinder, whose height is 0.6 and has a radius of 0.2.
[tex]\stackrel{\textit{\large area of the rectangular prism}}{\stackrel{\textit{front and back}}{2(0.6\cdot 0.55)}+\stackrel{\textit{left and right}}{2(0.4\cdot 0.55)}+\stackrel{bottom}{(0.4\cdot 0.6)}}\implies \boxed{1.34} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{total area of a cylinder}\\\\ A=2\pi r(h+r) \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=0.2\\ h=0.6 \end{cases}\implies \begin{array}{llll} A=2(\stackrel{\pi }{3.14})(0.2)(0.6+0.2)\\\\ A=1.0048\\\\ \stackrel{\textit{half that for a half-cylinder}}{\boxed{0.5024}} \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1.34+0.5024\implies 1.8424\implies \stackrel{\textit{rounded up}}{2~m^2}[/tex]
