Question

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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Answer 1

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 units²
2. **Perimeter**: 36 units