https://file.aiquickdraw.com/mathbot/file/1727319016770ct229h4e.jpg

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.

Find the perimeter of square BCDE using coordinate geometry. This problem involves finding the length of a side using the coordinates of vertices and applying the perimeter formula. Suitable for students in Grades 6-8.

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