To reduce to practical sizes, a ground plane in normally, again, based on 1/4 wavelength. For a transponder or ADSB monopole antenna, the ground plane radius needs to be a minimum of 2.6". So you can have a circular ground plane with that radius or a 5.2" x 5.2" square.

For the VHF radio it needs to bigger, since the frequency is a lot lower. Taking 118MHz as the lowest VHF frequency for our radios gives us a 1/4 wavelength of 23.8".

Of course, you don't actually need a square or circle of aluminium/some other metal. You can choose to 4 strips of metal or foil radiating out from the antenna. This might be useful for someone with a composite structure in which the antenna can be securely mounted. However, for fabric covered aircraft it is normal to use a 'complete' ground plane because it can then also be used to provide structure and strength to mount the aerial.