To find the area of the shaded region, we have to subtract the area of the parallelogram and the area of the rectangle. Let's find the area of each figure.
[tex]A_{\text{parallelogram}}=bh[/tex]
The base of the parallelogram is 4m and the height is 6m.
[tex]A_{\text{parallelogram}}=4m\cdot6m=24m^2[/tex]
Now let's find the area of the rectangle.
[tex]A_{\text{rectangle}}=bh[/tex]
The base of the rectangle is 3m and the height is 2m.
[tex]A_{\text{rectangle}}=3m\cdot2m=6m^2[/tex]
Once we have the area of each figure, let's subtract.
[tex]\begin{gathered} A_{\text{shaded}}=A_{\text{parallelogram}}-A_{\text{rectangle}} \\ A_{\text{shaded}}=24m^2-6m^2=18m^2 \end{gathered}[/tex]
Therefore, the area of the shaded region is 18 m^2.
