To compute the area of a rectangle defined by the given coordinates, we need to identify the lengths of its sides.
The coordinates provided are:
- \( a = (4, 2) \)
- \( b = (10, 4) \)
- \( c = (6, 16) \)
- \( d = (0, 14) \)
First, we determine the minimum and maximum x-coordinates and y-coordinates from these points.
- The minimum x-coordinate is \( \min(4, 10, 6, 0) = 0 \).
- The maximum x-coordinate is \( \max(4, 10, 6, 0) = 10 \).
- The minimum y-coordinate is \( \min(2, 4, 16, 14) = 2 \).
- The maximum y-coordinate is \( \max(2, 4, 16, 14) = 16 \).
The width of the rectangle (distance between maximum and minimum x-coordinates) is: \[ \text{Width} = \text{max x} - \text{min x} = 10 - 0 = 10 \]
The height of the rectangle (distance between maximum and minimum y-coordinates) is: \[ \text{Height} = \text{max y} - \text{min y} = 16 - 2 = 14 \]
Now, we can calculate the area of the rectangle: \[ \text{Area} = \text{Width} \times \text{Height} = 10 \times 14 = 140 \text{ units}^2 \]
Thus, the approximate area of the rectangle, rounded to the nearest whole number, is: \[ \boxed{140} \text{ units}^2 \]