To find the area and perimeter of the rectangle formed by points A, B, C, and D, we first need to determine the lengths of the sides of the rectangle.
The points given are:
- D (0, 14)
- C (6, 16)
- B (10, 4)
- A (4, 2)
Finding the Dimensions of the Rectangle:
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Finding the length of the rectangle: To determine the length, we can find the distance between two vertical points, say A (4, 2) and B (10, 4) (both horizontal coordinates lie along a vertical line between x = 4 and x = 10).
- Length = x-coordinate of B - x-coordinate of A = 10 - 4 = 6 units
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Finding the width of the rectangle: To find the width, we need to determine the vertical distance between the points D (0, 14) and A (4, 2) (both vertical coordinates lie along a horizontal line between y = 2 and y = 14).
- Width = y-coordinate of D - y-coordinate of A = 14 - 2 = 12 units
Question 1: Area of the Rectangle
The area \(A\) of a rectangle is calculated using the formula: \[ A = \text{Length} \times \text{Width} \] Substituting the length and width we found: \[ A = 6 \times 12 = 72 \text{ units}^2 \]
So, the area rounded to the nearest whole number is 72 units².
Question 2: Perimeter of the Rectangle
The perimeter \(P\) of a rectangle is calculated using the formula: \[ P = 2 \times (\text{Length} + \text{Width}) \] Using the length and width we found: \[ P = 2 \times (6 + 12) = 2 \times 18 = 36 \text{ units} \]
So, the perimeter rounded to the nearest whole number is 36 units.
Final Answers:
- Area: 72 units²
- Perimeter: 36 units
1 answer