Final answer:
The length of the side of the square is 6sqrt(2). The area of the square is 72 square units. The perimeter of the square is 24sqrt(2) units.
Step-by-step explanation:
To find the area and perimeter of a square, we need to know the length of one side of the square. Given the coordinates of the two endpoints of the diagonal, we can find the length by using the distance formula. The distance formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
By plugging in the values, we get:
distance = sqrt((2 - (-4))^2 + (-3 - 3)^2) = sqrt(6^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72) = 6sqrt(2)
Since the diagonal of a square divides it into two congruent right isosceles triangles, the length of the diagonal is equal to the hypotenuse of each triangle. Thus, the length of one side of the square is 6sqrt(2).
To find the area of the square, we can use the formula: area = side length * side length.
area = (6sqrt(2))^2 = 36 * 2 = 72 square units.
To find the perimeter of the square, we can use the formula: perimeter = 4 * side length.
perimeter = 4 * 6sqrt(2) = 24sqrt(2) units.
Learn more about Calculating the area and perimeter of a square