The ant walks in a circular path from center A to point B, then to point C, and finally back to center A. The total distance of her walk is equal to the circumference of the circle that passes through points A, B, and C.
To find the circumference, we need to know the radius of the circle. We can use the Pythagorean theorem to find the radius:
r^2 = AB^2 + BC^2
r^2 = (2 cm)^2 + (2 cm)^2
r^2 = 4 cm^2 + 4 cm^2
r^2 = 8 cm^2
r = sqrt(8) cm
r = 2 sqrt(2) cm
Now we can use the formula for the circumference of a circle:
C = 2πr
C = 2π(2 sqrt(2) cm)
C = 4π sqrt(2) cm
So the total distance of the ant's walk is approximately 17.77 cm (4π sqrt(2) cm).