To find the area and perimeter of the rectangle defined by the coordinates of the points A, B, C, and D, we first need to identify the coordinates of the points:
- \( A = (4, 2) \)
- \( B = (10, 4) \)
- \( C = (6, 16) \)
- \( D = (0, 14) \)
Step 1: Determine the rectangle's base and height
To determine the dimensions of the rectangle, we identify the highest and lowest y-values among the points (which will define the height) and the leftmost and rightmost x-values (which will define the width).
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Width:
- The x-values for the points are 4, 10, 6, and 0.
- The leftmost point is \( D(0, 14) \) and the rightmost is \( B(10, 4) \), so the width is: \[ \text{Width} = 10 - 0 = 10 \]
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Height:
- The y-values for the points are 2, 4, 16, and 14.
- The lowest point is \( A(4, 2) \) and the highest is \( C(6, 16) \), so the height is: \[ \text{Height} = 16 - 2 = 14 \]
Step 2: Calculate the area of the rectangle
The area \( A \) of a rectangle is calculated as: \[ A = \text{Width} \times \text{Height} = 10 \times 14 = 140 \]
So, the area of the rectangle is 140 square units.
Step 3: Calculate the perimeter of the rectangle
The perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{Width} + \text{Height}) = 2(10 + 14) = 2 \times 24 = 48 \]
So, the perimeter of the rectangle is 48 units.
Final Answers:
- Area: 140 units²
- Perimeter: 48 units
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