To compute the area of the rectangle defined by the given coordinates \( a \), \( b \), \( c \), and \( d \), we first need to identify the coordinates that represent the bottom-left and top-right corners of the rectangle.
The coordinates are:
- \( a = (4, 2) \) (bottom-left)
- \( b = (10, 4) \) (top-right)
- \( c = (6, 16) \) (top-left)
- \( d = (0, 14) \) (bottom-right)
However, let's clarify which points can actually represent the corners of a rectangle and whether they can be connected in a way to form a rectangle.
To get the dimensions of the rectangle, we can use the x-coordinates and y-coordinates:
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The width (length along the x-axis) is given by the difference between the maximum and minimum x-coordinates: \[ \text{Width} = \text{max}(x_a, x_b, x_c, x_d) - \text{min}(x_a, x_b, x_c, x_d) = \text{max}(4, 10, 6, 0) - \text{min}(4, 10, 6, 0) = 10 - 0 = 10 \]
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The height (length along the y-axis) is given by the difference between the maximum and minimum y-coordinates: \[ \text{Height} = \text{max}(y_a, y_b, y_c, y_d) - \text{min}(y_a, y_b, y_c, y_d) = \text{max}(2, 4, 16, 14) - \text{min}(2, 4, 16, 14) = 16 - 2 = 14 \]
Next, we calculate the area of the rectangle: \[ \text{Area} = \text{Width} \times \text{Height} = 10 \times 14 = 140 \]
Finally, rounding to the nearest whole number, the approximate area of the rectangle is: \[ \boxed{140} \]
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