check the picture below
if the width or base of the rectangle is 3 units, that means the diameter of the semi-circle is 3, and thus the radius is half that, notice the red radius line
the area of the figure is the area of the rectangle 3x4, plus the area of the semi-circle
[tex]\bf \textit{area of a circle}\\\\
A=\pi r^2\\\\
-------------------------------\\\\
\textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2}\qquad
\begin{cases}
r=radius\\
-----\\
r=\frac{3}{2}
\end{cases}\implies A=\cfrac{\pi \frac{3^2}{2^2}}{2}\implies A=\cfrac{\frac{9\pi }{4}}{\frac{2}{1}}
\\\\\\
A=\cfrac{9\pi }{4}\cdot \cfrac{1}{2}\implies A=\cfrac{9\pi }{8}[/tex]
