To compute the approximate area of a rectangle given the provided coordinates, we first need to identify the extremes of the coordinates, specifically the minimum and maximum values for both x and y coordinates.
The points given are:
- \( A(3, 1) \)
- \( B(-3, -1) \)
- \( C(-2, -4) \)
- \( D(4, -2) \)
Step 1: Find the extremes of the coordinates.
-
The minimum and maximum x-coordinates:
- Min \( x \) = \( -3 \) (from point B)
- Max \( x \) = \( 4 \) (from point D)
-
The minimum and maximum y-coordinates:
- Min \( y \) = \( -4 \) (from point C)
- Max \( y \) = \( 1 \) (from point A)
Step 2: Calculate the lengths of the sides of the rectangle.
-
Length of the rectangle along the x-axis: \[ \text{Length} = \text{Max } x - \text{Min } x = 4 - (-3) = 4 + 3 = 7 \]
-
Length of the rectangle along the y-axis: \[ \text{Width} = \text{Max } y - \text{Min } y = 1 - (-4) = 1 + 4 = 5 \]
Step 3: Calculate the area of the rectangle. \[ \text{Area} = \text{Length} \times \text{Width} = 7 \times 5 = 35 \]
Thus, the approximate area of the rectangle formed by the given coordinates is \( \boxed{35} \).