Why A Yagi is built around a resonant dipole as its driven element, and a resonant dipole is a half wavelength long. The parasitic elements are sized relative to it: the reflector is roughly 5 percent longer and the directors a few percent shorter, which is what steers the pattern forward. In feet, a half-wave driven element is approximately 468 divided by the frequency in MHz.
Watch out The 234 divided by frequency formula gives a quarter wavelength in feet, which is the length of one leg of a dipole or of a ground-mounted vertical, not the whole driven element; 1005 divided by frequency is closer to a full wavelength and is used for loop antennas.
Driven element = dipole = half wave. 468/f(MHz) feet; 234/f is only one leg.