Final answer:
The area of the quadrilateral with the given vertices is 9√2
Step-by-step explanation:
To find the area of the quadrilateral with the vertices W(3,0), X(0,3), Y(-3,0), and Z(0,-3), we can divide it into two triangles and calculate their individual areas.
Triangle WXZ has vertices W(3,0), X(0,3), and Z(0,-3). We can use the formula for the area of a triangle: A = 1/2 * base * height. The base of WXZ is the distance between W and X, which is √(3^2 + 3^2) = 3√2. The height is the distance between Z and the line passing through W and X, which is 3. So, the area of WXZ is 1/2 * 3√2 * 3 = 4.5√2.
Similarly, triangle WYZ has vertices W(3,0), Y(-3,0), and Z(0,-3). The base of WYZ is the distance between W and Y, which is √(3^2 + 3^2) = 3√2. The height is the distance between Z and the line passing through W and Y, which is 3. So, the area of WYZ is 1/2 * 3√2 * 3 = 4.5√2.
Therefore, the total area of the quadrilateral is the sum of the areas of the two triangles: 4.5√2 + 4.5√2 = 9√2.