Final answer:
The perimeter of square ABCD can be calculated by finding the length of one side using the distance formula and then multiplying it by 4, because a square has equal side lengths. The calculated approximate perimeter is 11.32 units.
Step-by-step explanation:
To find the perimeter of square ABCD with vertices A(-2,2), B(0,4), C(2,2), and D(0,0), we must calculate the length of one side of the square because the lengths of all four sides in a square are equal. We can choose any two adjacent vertices to calculate the length of a side. For instance, to find the length between A and B, we can apply the distance formula which is √((x2 - x1)² + (y2 - y1)²). Using this formula:
- Length AB = √((0 - (-2))² + (4 - 2)²) = √(2² + 2²) = √8
The exact length of AB is √8, which approximates to 2.83 units. Since all sides of a square are equal, the perimeter will be 4 times the length of one side:
- Perimeter of square ABCD = 4 x 2.83 = 11.32 units
The correct answer from the given options is B. 11.31, which is a rounded-off value of the exact perimeter.