To compute the approximate area of the rectangle formed by the points A, B, C, and D, we first need to identify which points are corners of the rectangle.
Given the coordinates:
- Point A: (4, 2)
- Point B: (10, 4)
- Point C: (6, 16)
- Point D: (0, 14)
We can check the x and y coordinates to find the extremes for width and height:
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The x-coordinates are 4, 10, 6, and 0.
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The minimum x-coordinate is 0 (from Point D) and the maximum x-coordinate is 10 (from Point B).
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The y-coordinates are 2, 4, 16, and 14.
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The minimum y-coordinate is 2 (from Point A) and the maximum y-coordinate is 16 (from Point C).
Now we can calculate the width and height of the rectangle:
- Width (horizontal distance) = maximum x - minimum x = 10 - 0 = 10
- Height (vertical distance) = maximum y - minimum y = 16 - 2 = 14
Now, we can calculate the area of the rectangle: \[ \text{Area} = \text{Width} \times \text{Height} = 10 \times 14 = 140 \]
Rounding to the nearest whole number, the approximate area of the rectangle is \( 140 \).
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