To determine the area of the figure you have to decompose it into two simpler figures:
A semicircle (green) and a rectangle (blue)
The total area of the figure is equal to the area of the semicircle plus the area of the rectangle
[tex]A_T=A_C+A_R[/tex]
The area of the rectangle can be calculated as
[tex]\begin{gathered} A_R=w\cdot l \\ A_R=6\cdot12 \\ A_R=72 \end{gathered}[/tex]
The area of a circle can be calculated as
[tex]\text{Acircle}=\pi r^2[/tex]
To calculate the area of the semicircle you have to divide it by 2
[tex]A_C=\frac{\pi r^2}{2}[/tex]
The semicircle has a diameter of d=6
So the radius is
[tex]r=\frac{d}{2}=\frac{6}{2}=3[/tex]
The area of the semicircle is
[tex]\begin{gathered} A_C=\frac{\pi r^2}{2} \\ A_C=\frac{\pi3^2}{2} \\ A_C=\frac{9}{2}\pi \end{gathered}[/tex]
Finally add both areas to determine the area of the figure
[tex]\begin{gathered} A_T=A_R+A_C \\ A_T=72+\frac{9}{2}\pi \\ A_T=86.137\cong86.1 \end{gathered}[/tex]
The total area of the figure is 86.1
