Just over two years of age. The average height of an adult American male is 1.77 meters, so half that would be 88.5 cm. This level is reached at about 2 years 3 months. For females, who grow at similar rates as small children but have a slightly lower end height, the threshold will be reached a little earlier.
Three quarters (134 cm for boys) is reached around age 9.
The numbers are taken from this chart: