Why A Yagi is built around a resonant dipole as its driven element, and a dipole is about a half wavelength long. In practical terms that is roughly 468 divided by the frequency in MHz, in feet. The parasitic elements are sized relative to that: the reflector is about 5 percent longer and the directors about 5 percent shorter.
Watch out The quarter wavelength choice describes a vertical or ground-plane element, which uses the ground or radials to supply the missing half of the dipole; a Yagi's driven element stands alone as a full dipole.
Yagi driven element = a dipole = 1/2 wavelength. Reflector longer, directors shorter.