Question

What is the area, in square units, of the polygon plotted on the coordinate plane below?

Answer 1

Area = 20 square units

Step-by-step 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:

`\begin{gathered} Area(polygon)=Area_(rectangle,1)+Area_(rectangle,2) \\ Area_(rectangle,1)=length_1* width_1 \\ Area_(rectangle,2)=length_2* 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*2)+(3*2) \\ Area(polygon)=14+6 \\ Area(polygon)=20units^2 \\ \\ \therefore Area(polygon)=20units^2 \end{gathered}`

Therefore, the area of the polygon is 20 square units