being purely a mechanical engineer, I would agree, (on the basis of the picture) with the likelihood of the Antenna input being 300 ohm, and with the need to match the antenna and connecting cable impedance to that of the set, to maximise power transfer.
Radio hams usually opt for "as high as possible" for antenna positioning, and in alignment with the transmitter.
At 225MHz the elements of a yagi are going to be pretty short, (digital TV is around 240 / 250 MHz from memory,
So your radio antenna is going to be only a bit larger. A folded dipole is likely be even smaller, end to end.
The data already posted plus a bit of calculation should allow you make reasonable antenna, and position it for best reception.
Having said all this, I very rarely switch on the FM radio in my shop! Too busy metal mangling!
Howard