Answer:
Area = 20 square units
Explanation:
From the plot, we will observe that the polygon is a compound figure comprised of 2 rectangles separated by the red line (diagram below)
We will calculate the area of the polygon by summing the areas of the two rectangles as shown below:
[tex]\begin{gathered} Area(polygon)=Area_{rectangle,1}+Area_{rectangle,2} \\ Area_{rectangle,1}=length_1\times width_1 \\ Area_{rectangle,2}=length_2\times width_2 \\ length_1=2-(-5)=2+5=7units \\ width_1=-2-(-4)=-2+4=2units \\ length_2=-4-(-7)=-4+7=3units \\ width_2=0-(-2)=0+2=2units \\ \text{Substituting these into the formula for ''Area'' above, we have:} \\ Area(polygon)=(7\times2)+(3\times2) \\ Area(polygon)=14+6 \\ Area(polygon)=20units^2 \\ \\ \therefore Area(polygon)=20units^2 \end{gathered}[/tex]
Therefore, the area of the polygon is 20 square units
