Rectangle $$ A B C D $$ has consecutive vertices $$ A(-5,2), B(-5,7), C(1,7 $$ and $$ D(1,2) $$. Find the perimeter and area of rectangle $$ A B C D $$.

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To determine the perimeter and area of rectangle $$ A B C D $$ with vertices $$ A(-5,2) $$, $$ B(-5,7) $$, $$ C(1,7) $$, and $$ D(1,2) $$, we'll follow these steps:

### 1. Determine the Lengths of the Sides

**Side $$ AB $$:**
- Both points $$ A(-5,2) $$ and $$ B(-5,7) $$ have the same $$ x $$-coordinate.
- This means side $$ AB $$ is vertical.
- The length of $$ AB $$ is the difference in the $$ y $$-coordinates:
  $$
  AB = |7 - 2| = 5 \text{ units}
  $$

**Side $$ BC $$:**
- Both points $$ B(-5,7) $$ and $$ C(1,7) $$ have the same $$ y $$-coordinate.
- This means side $$ BC $$ is horizontal.
- The length of $$ BC $$ is the difference in the $$ x $$-coordinates:
  $$
  BC = |1 - (-5)| = 6 \text{ units}
  $$

### 2. Calculate the Perimeter

The perimeter $$ P $$ of a rectangle is given by:
$$
P = 2 \times (\text{length} + \text{width}) = 2 \times (AB + BC)
$$
Substituting the values:
$$
P = 2 \times (5 + 6) = 2 \times 11 = 22 \text{ units}
$$

### 3. Calculate the Area

The area $$ A $$ of a rectangle is given by:
$$
A = \text{length} \times \text{width} = AB \times BC
$$
Substituting the values:
$$
A = 5 \times 6 = 30 \text{ square units}
$$

### **Final Answer:**
- **Perimeter:** $$ 22 $$ units
- **Area:** $$ 30 $$ square units
The perimeter of rectangle $$ A B C D $$ is 22 units, and the area is 30 square units.

Rectangle has consecutive vertices
and . Find the perimeter and area of rectangle .

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Rectangle has consecutive vertices and . Find the perimeter and area of rectangle .