To find the perimeter of the square $BCDE$, we need to calculate the length of one side of the square and then multiply that by 4 (since all sides of a square are equal).

Step 1: Identify the coordinates of the vertices

From the image, the coordinates of points are approximately:

• $B(-6, 6)$
• $C(-6, -6)$
• $D(6, -6)$
• $E(6, 6)$

Step 2: Calculate the side length

The length of one side of the square can be calculated by finding the distance between two adjacent vertices. For example, the distance between $B(-6, 6)$ and $E(6, 6)$ (or similarly between $C$ and $D$) is the difference in their $x$-coordinates (since their $y$-coordinates are the same):

$\text{Side length} = |6 - (-6)| = 12 \text{ units}$

Step 3: Calculate the perimeter

The perimeter $P$ of a square is given by:

$P = 4 \times \text{side length} = 4 \times 12 = 48 \text{ units}$

Final Answer:

The perimeter of square $BCDE$ is $48$ units.

Would you like any more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you calculate the distance between two points in a coordinate plane?
2. What is the formula for finding the perimeter of a square?
3. Can the perimeter formula be applied to other shapes, such as rectangles or triangles?
4. How would the perimeter change if the square was scaled by a factor of 2?
5. How do we determine the area of square $BCDE$ given its side length?

Tip: When finding the distance between two points that are aligned horizontally or vertically, you only need to subtract their respective coordinates along the direction in which they differ.