Question

find the area of the polygon with the given vertices. w(0, 0), x(0, 3), y(- 3, 3), z(- 3, 0)
the area is square units.

Explanation:

Step1: Identify the polygon type

The polygon with vertices $W(0,0), X(0,3), Y(- 3,3), Z(-3,0)$ is a rectangle. The length of one - side can be found by calculating the distance between two points.

Step2: Calculate the length of the sides

The distance between $W(0,0)$ and $X(0,3)$ is $d_{WX}=\vert3 - 0\vert=3$ (using the distance formula for points with the same x - coordinate $d=\vert y_2 - y_1\vert$). The distance between $X(0,3)$ and $Y(-3,3)$ is $d_{XY}=\vert-3 - 0\vert = 3$ (using the distance formula for points with the same y - coordinate $d=\vert x_2 - x_1\vert$).

Step3: Use the area formula for a rectangle

The area formula for a rectangle is $A = l\times w$. Here, $l = 3$ and $w = 3$. So $A=3\times3 = 9$.

Answer:

9