To find the area and perimeter of the rectangle formed by points A (4,2), B (10,4), C (6,16), and D (0,14), we first need to understand the coordinates of the rectangle and which points are the vertices.
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Identifying the vertices of the rectangle:
- Points A (4,2) and B (10,4) can be one pair of vertices.
- The coordinates suggest that the rectangle might not be aligned with the axes, so it helps to find the lengths of the sides.
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Calculating the lengths of the sides:
- Length of one side (horizontal) between A and B:
- Distance between A (4,2) and B (10,4): \[ \text{Length (side AB)} = x_B - x_A = 10 - 4 = 6 \]
- The vertical sides can be calculated between points A and D and points B and C:
- Vertical side (between A and D): \[ \text{Length (side AD)} = y_D - y_A = 14 - 2 = 12 \]
- Vertical side (between B and C): \[ \text{Length (side BC)} = y_C - y_B = 16 - 4 = 12 \]
- Length of one side (horizontal) between A and B:
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Area of the rectangle: The area \( A \) of a rectangle can be calculated as: \[ A = \text{length} \times \text{width} = 6 \times 12 = 72 \]
Rounding to the nearest whole number, the area is: \[ \text{Area} \approx 72 , \text{units}^2 \]
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Perimeter of the rectangle: The perimeter \( P \) is calculated as: \[ P = 2(\text{length} + \text{width}) = 2(6 + 12) = 2 \times 18 = 36 \]
Rounding to the nearest whole number, the perimeter is: \[ \text{Perimeter} \approx 36 , \text{units} \]
Answers:
- Area: 72 units²
- Perimeter: 36 units