The area of the composite shape is [tex]21\pi\text{ sq. units}[/tex]
The shape is made up of four semi-circular regions. (see image attached to the solution). The area can be computed as follows:
[tex]Area=(A-C)+(B-D)[/tex]
where each letter represents the areas of the associated semi-circles.
The area of a semi-circle is given by
[tex]Area_s=\dfrac{\pi r^2}{2}[/tex]
For region [tex]A[/tex], [tex]r=6units[/tex]
[tex]A=\dfrac{\pi\times6^2}{2}\\\\=18\pi \text{ sq.units}[/tex]
For region [tex]B[/tex], [tex]r=4units[/tex]
[tex]B=\dfrac{\pi\times4^2}{2}\\\\=8\pi \text{ sq.units}[/tex]
For region [tex]C[/tex], [tex]r=3units[/tex]
[tex]C=\dfrac{\pi\times3^2}{2}\\\\=4.5\pi \text{ sq.units}[/tex]
For region [tex]D[/tex], [tex]r=1units[/tex]
[tex]D=\dfrac{\pi\times1^2}{2}\\\\=0.5\pi \text{ sq.units}[/tex]
So, the area of the shape is
[tex]Area=(A-C)+(B-D)\\\\=[(18-4.5)+(8-0.5)]\pi\\\\=21\pi\text{ sq.units}[/tex]
Learn more about how to compute the area of composite shapes: https://brainly.com/question/316492
