Given the figure, the area of the rectangle is:
[tex]A_{\text{rectangle}}=6\cdot9=54cm^2[/tex]
Now, we need to subtract the areas of the semicircles from this. The areas of the semicircles are:
[tex]\begin{gathered} A_1=\pi\cdot\frac{2^2}{2}=2\pi cm^2 \\ A_2=\pi\cdot\frac{2.5^2}{2}=\frac{25\pi}{8}cm^2 \\ A_3=\pi\cdot\frac{2.5^2}{2}=\frac{25\pi}{8}cm^2 \end{gathered}[/tex]
Then, the area of the figure is:
[tex]A=A_{\text{rectangle}}-A_1-A_2-A_3_{}_{}[/tex]
Using the values of each area:
[tex]\begin{gathered} A=54-2\pi-\frac{25\pi}{8}-\frac{25\pi}{8}=(54-\frac{33\pi}{4})cm^2 \\ \Rightarrow A\approx28.082cm^2 \end{gathered}[/tex]
