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
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Distance CD: \[ CD = \sqrt{((-4) - (-5))^2 + (4 - 4)^2} = \sqrt{(1)^2 + (0)^2} = \sqrt{1} = 1 \]
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Distance DE: \[ DE = \sqrt{((-4) - (-4))^2 + (5 - 4)^2} = \sqrt{(0)^2 + (1)^2} = \sqrt{1} = 1 \]
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Distance EF: \[ EF = \sqrt{((-3) - (-4))^2 + (5 - 5)^2} = \sqrt{(1)^2 + (0)^2} = \sqrt{1} = 1 \]
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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):
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Distance CE: \[ CE = \sqrt{((-4) - (-5))^2 + (5 - 4)^2} = \sqrt{(1)^2 + (1)^2} = \sqrt{2} \]
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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
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Area: \[ \text{Area} = \text{length} \times \text{width} = 1 \times 1 = 1 \]
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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.