Question

What are the area and perimeter of square CDEF?
C =(-5,4)
D =(-4,4)
E = (-4,5)
F = (-3,5)

Answer 1

To determine the area and perimeter of square CDEF, we first need to verify that the points form a square and then calculate the side length.

### Step 1: Check the given points

The points are:
- C = (-5, 4)
- D = (-4, 4)
- E = (-4, 5)
- F = (-3, 5)

### Step 2: Calculate the distances between adjacent points

1. Distance CD:
\[
CD = \sqrt{((-4) - (-5))^2 + (4 - 4)^2} = \sqrt{(1)^2 + (0)^2} = \sqrt{1} = 1
\]

2. Distance DE:
\[
DE = \sqrt{((-4) - (-4))^2 + (5 - 4)^2} = \sqrt{(0)^2 + (1)^2} = \sqrt{1} = 1
\]

3. Distance EF:
\[
EF = \sqrt{((-3) - (-4))^2 + (5 - 5)^2} = \sqrt{(1)^2 + (0)^2} = \sqrt{1} = 1
\]

4. Distance FC:
\[
FC = \sqrt{((-5) - (-3))^2 + (4 - 5)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5}
\]

### Step 3: Verify that the diagonals are equal (not necessarily needed for a square)

To confirm it's a square, we should check the diagonals (CE and DF):

1. Distance CE:
\[
CE = \sqrt{((-4) - (-5))^2 + (5 - 4)^2} = \sqrt{(1)^2 + (1)^2} = \sqrt{2}
\]

2. Distance DF:
\[
DF = \sqrt{((-3) - (-4))^2 + (5 - 4)^2} = \sqrt{(1)^2 + (1)^2} = \sqrt{2}
\]

### Conclusion

Based on the distances:
- The sides (CD, DE, EF, and FC) are not equal to each other, indicating that this shape is not a square, as necessary side lengths must correspond.
- However, if this is intended to be a rectangle or quadrilateral, we conclude it is a rectangle formed by points D and E being vertical while C and F being aligned horizontally.

### Calculate Area and Perimeter (assuming perpendicular sides)

**Side lengths identified earlier:**
- Horizontal side: \( CD = 1 \)
- Vertical side: \( DE = 1 \)

### Area and Perimeter Calculation

- **Area**:
\[
\text{Area} = \text{length} \times \text{width} = 1 \times 1 = 1
\]

- **Perimeter**:
\[
\text{Perimeter} = 2(\text{length} + \text{width}) = 2(1 + 1) = 4
\]

Thus, the area of square-like figure CDEF is **1** and the perimeter is **4**. However, this isn't a square due to the dimensions being not uniform.