To determine the area and perimeter of the rectangle, we first need to identify its dimensions based on the given points A(4, 2), B(10, 4), C(6, 16), and D(0, 14).
Step 1: Identify the rectangle's dimensions.
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Calculate length (horizontal distance):
- The x-coordinates of points B (10, 4) and A (4, 2) show that B is further right than A.
- Length = x-coordinate of B - x-coordinate of A = 10 - 4 = 6 units.
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Calculate width (vertical distance):
- The y-coordinates of points A (4, 2) and D (0, 14) can be compared to find the vertical distance.
- Width = y-coordinate of D - y-coordinate of A = 14 - 2 = 12 units.
Step 2: Calculate the area.
Area of a rectangle = length × width
- Area = 6 units × 12 units = 72 square units.
Step 3: Calculate the perimeter.
Perimeter of a rectangle = 2 × (length + width)
- Perimeter = 2 × (6 + 12) = 2 × 18 = 36 units.
Final Answers:
- Area: 72 units²
- Perimeter: 36 units