To find the area and perimeter of the rectangle defined by the points A(4,2), B(10,4), C(6,16), and D(0,14), we must first establish which points are the vertices of the rectangle, which they are not as they do not form right angles typically associated with rectangles. Therefore, the correct shape may not be a rectangle. However, if we can identify the arrangement, we could approximate the rectangle by finding appropriate pairs for the length and width.
Since the given points do not directly correspond to the vertices of a rectangular shape, here is an approach using the two possible lengths derived as vertical and horizontal distances using two identified points:
Using points A(4, 2) and C(6, 16):
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Length (vertical distance): \[ \text{Length} = |y_2 - y_1| = |16 - 2| = 14 \]
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Width (horizontal distance): \[ \text{Width} = |x_2 - x_1| = |6 - 4| = 2 \]
Area
The area \( A \) of a rectangle is calculated by the formula: \[ A = \text{length} \times \text{width} \] \[ A = 14 \times 2 = 28 \]
Perimeter
The perimeter \( P \) of a rectangle is calculated by the formula: \[ P = 2(\text{length} + \text{width}) \] \[ P = 2(14 + 2) = 2 \times 16 = 32 \]
Summary
- Area = 28 square units (rounded to the nearest whole number)
- Perimeter = 32 units (rounded to the nearest whole number)
Thus:
- Question 1: 28 units²
- Question 2: 32 units
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