Final answer:
The area of the rectangle with the given vertices is 16.9 square units.
Step-by-step explanation:
To find the area of a rectangle, we can use the formula:
Area = Length × Width
In this case, the given coordinates represent the vertices of the rectangle. We can find the length by subtracting the x-coordinates of two adjacent vertices and the width by subtracting the y-coordinates of two adjacent vertices. Once we have the length and width, we can multiply them to find the area.
Let's calculate the area using the given coordinates:
Length (L) = x-coordinate of (-4, 2.31) - x-coordinate of (6, 3) = -4 - 6 = -10
Width (W) = y-coordinate of (-4, 2.31) - y-coordinate of (-2, 4) = 2.31 - 4 = -1.69
Since length and width cannot be negative values, we take the absolute values:
Length (L) = |-10| = 10
Width (W) = |-1.69| = 1.69
Finally, we can calculate the area:
Area = Length × Width = 10 × 1.69 = 16.9 square units