Answer: 10
Step-by-step explanation:
If you graph the polygon, you will see that it is a rectangle with length = 5 and width = 2. Using the area formula for a rectangle: A = Length x width
A = 5 × 2
= 10
If you don't graph it, then you need to find the distance between the points.
[tex]d_{NP}=\sqrt{(x_N-x_p)^2+(y_N-y_P)^2}\\\\.\ \ \quad =\sqrt{(3+2)^2+(1-1)^2}\\\\.\ \ \quad =\sqrt{5^2+0^2}\\\\.\ \ \quad =\sqrt{25}\\\\.\ \ \quad =5\\\\\\d_{PQ}=\sqrt{(x_P-x_Q)^2+(y_P-y_Q)^2}\\\\.\ \ \quad =\sqrt{(3-3)^2+(1+1)^2}\\\\.\ \ \quad =\sqrt{0^2+2^2}\\\\.\ \ \quad =\sqrt{4}\\\\.\ \ \quad =2[/tex]
Continue by finding the distance from Q to R (which equals 5) and the distance from R to N (which equals 2), which shows that this polygon is a rectangle. Then use the area formula: A = NP × PQ
= 5 × 2
= 10
