Find the perimeter of the square kira with vertices k(-6,2), i(2, -4), r(-4, -12), and a (-12, -6)

The answer is 40 units.

Let's first calculate the distance between the vertices. This is the square so all distances are equal.
The distance formula is derived from the Pythagorean theorem:
d = √((x2 - x1)² + (y2 - y1)²)

Let use points K(-6,2) and I(2, -4):
x1 = -6
x2 = 2
y1 = 2
y2 = -4

d = √((2 - (-6))² + (-4 - 2)²)
d = √(8² + 6²)
d = √(64 + 36)
d = √100
d = 10 units

Now, the perimeter of the square is:
P = 4d = 4 * 10 = 40 units