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To calculate the perimeter of square \( CDEF \), we need to determine the length of one side and then multiply that by 4, since the perimeter \( P \) of a square is given by:

\[
P = 4 \times \text{side length}
\]

### Step 1: Find the side length of the square.

We can use the distance formula to find the length of any side. Let's calculate the distance between two consecutive vertices, say \( C(10, -2) \) and \( D(4, -6) \).

The distance formula is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of \( C \) and \( D \):

\[
d = \sqrt{(4 - 10)^2 + (-6 - (-2))^2}
\]
\[
d = \sqrt{(-6)^2 + (-4)^2}
\]
\[
d = \sqrt{36 + 16} = \sqrt{52} \approx 7.21
\]

So, the side length of the square is approximately 7.21 units.

### Step 2: Calculate the perimeter.

Now, we multiply the side length by 4:

\[
P = 4 \times 7.21 = 28.84 \text{ units}
\]

Thus, the perimeter of square \( CDEF \) is approximately **28.8 units** (rounded to the nearest tenth).

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Would you like more details or have any questions?

### Related Questions:
1. How would you calculate the area of square \( CDEF \)?
2. Can you find the coordinates of the center of the square?
3. What is the distance from point \( E \) to point \( F \)?
4. How do you determine if four points form a square using their coordinates?
5. How would the perimeter change if the square were scaled by a factor of 2?

### Tip:
Always double-check whether the shape is truly a square by ensuring all sides are equal and the diagonals intersect at right angles.

What is the perimeter of square CDEF with coordinates C(10, -2), D(4, -6), E(0, 0), F(6, 4)?

Calculate the perimeter of square CDEF by applying the distance formula between points C(10, -2) and D(4, -6). Learn key concepts in geometry, including how to determine side length and compute the perimeter of a square. This problem is ideal for students in Grades 8-10.

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