Question 1

(1 point)
What is the area of the rectangle shown above? Round your answer to the nearest whole number A (4,2), B (10,4) C (6,16), and D(0,14)

units2

Question 2
What is the perimeter of the rectangle shown above? Round your answer to the nearest whole number. (1 point)
perimeter =
units
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1 answer

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.

  1. 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.
  2. 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): \[ \text{Length (side BC)} = y_C - y_B = 16 - 4 = 12 \]
  3. 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: \[ \text{Area} \approx 72 , \text{units}^2 \]

  4. 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:

  1. Area: 72 unitsĀ²
  2. Perimeter: 36 units