From the image, the problem asks to find the perimeter and area of a rectangle with given vertices $(-2, -1)$, $(-2, -5)$, $(4, -1)$, and $(4, -5)$.

Steps to Solve:

1. Identify the sides of the rectangle:

• The vertical sides are determined by the $y$-coordinates. The distance between $(-2, -1)$ and $(-2, -5)$ is: $\text{Height} = |-1 - (-5)| = 4 \text{ units}$
• The horizontal sides are determined by the $x$-coordinates. The distance between $(-2, -1)$ and $(4, -1)$ is: $\text{Width} = |4 - (-2)| = 6 \text{ units}$

2. Perimeter of the rectangle:

The formula for the perimeter $P$ of a rectangle is: $P = 2 \times (\text{Length} + \text{Width})$ Substituting the values: $P = 2 \times (6 + 4) = 2 \times 10 = 20 \text{ units}$

3. Area of the rectangle:

The formula for the area $A$ of a rectangle is: $A = \text{Length} \times \text{Width}$ Substituting the values: $A = 6 \times 4 = 24 \text{ square units}$

Final Answer:

• Perimeter: 20 units
• Area: 24 square units

Would you like more details or have any other questions?

Here are 5 related questions:

1. How do you calculate the perimeter and area of irregular polygons?
2. How does the formula for area differ for triangles versus rectangles?
3. What is the significance of the distance formula in finding side lengths of geometric shapes?
4. Can a rectangle have sides of equal length? How does that affect its properties?
5. How do you calculate the diagonal of a rectangle given its side lengths?

Tip: Always check the coordinates carefully when calculating distances between points to avoid sign errors!