Final answer:
The task was to find the area of rectangle ABCD, but upon calculation, it was discovered that the given coordinates do not form a rectangle because the sides are not perpendicular. Hence, it is not possible to calculate the area based on the provided coordinates.
Step-by-step explanation:
The problem requires us to find the area of rectangle ABCD. To find the area, we need to calculate the lengths of two adjacent sides (width and height) of the rectangle. We can do this by using the distance formula between two points, which is √((x2 - x1)² + (y2 - y1)²). By choosing pairs of points that form the sides, we can find the width and height.
Let's start by finding the width using points B(-2, -3) and C(2, -2). Applying the distance formula gives us the width:
Width = √((2 - (-2))² + (-2 - (-3))²) = √(16 + 1) = √17
Next, we'll find the height using points A(-4, 5) and B(-2, -3):
Height = √((-2 - (-4))² + (-3 - 5)²) = √(4 + 64) = √68
The area of rectangle ABCD is then the width times the height.
Area = Width × Height = √17 × √68
However, we might have made a mistake because points A, B, C, and D do not form a rectangle since AB is not perpendicular to BC (in fact, all pairs in these points form diagonal lines rather than sides of a rectangle). We cannot calculate the area since the given coordinates do not represent a rectangle.