Question

Ind the area of the polygon with the given vertices. N(−2, 1), P(3, 1), Q(3,−1), R(−2,−1)

Answer 1

Answer: 10

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.

`d_(NP)=√((x_N-x_p)^2+(y_N-y_P)^2)\\\\.\ \ \quad =√((3+2)^2+(1-1)^2)\\\\.\ \ \quad =√(5^2+0^2)\\\\.\ \ \quad =√(25)\\\\.\ \ \quad =5\\\\\\d_(PQ)=√((x_P-x_Q)^2+(y_P-y_Q)^2)\\\\.\ \ \quad =√((3-3)^2+(1+1)^2)\\\\.\ \ \quad =√(0^2+2^2)\\\\.\ \ \quad =√(4)\\\\.\ \ \quad =2`

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