The Public Broadcasting Service will buy approximately four acres near the Bren Mar subdivision in Fairfax County from Shell Oil Co. for $237,319.50 as part of a $39.5 million project to transmit programs via satellite.

Final approval for the purchase came Friday from the board of directors of the Corporation for Public Broadcasting which must approve expenditures for each part of the project.

PBS, with funding from CPB, will build an underground "main origination terminal" on the site that will permit it to send its 250-plus stations throughout the country several programs at one time.

PBS now sends most of its programming to stations through a combination of wires and microwave links. It also can mail tapes of programs to the stations, and in fact that is now the only means of sending programs to stations in Alaska, Hawaii, Puerto Rico and the Virgin Islands.

In addition to the Bren Mar installation, which is expected to cost $2.6 million, PBS will spend approximately $25.4 million on ground antennae for all but 14 of its stations so that they will be able to receive signals from the satellites. The 14 stations that will not have ground antennae are close to other PBS stations and have agreed to share their facilities.

Equipment to enable PBS to transmit signals via microwave from its facilities in the basement of L'Enfant Plaza to the Bren Mar installation will cost more than $500,000. Additional equipment - primarily tape machines - to give the technical section the capacity to broadcast several programs at the same time will run another $1.8 million.

Five regional origination terminals will complete the project at an approximate cost of $1.3 rillion. These will allow programming that originates in other parts of the country to be sent by satellite throughout the region or the nation.

The network said regional terminals will greatly increase its flexibility. It is now able to originate programs from only about three cities. Some regional systems - most of which are in the Northeast - also can originate programming.

Simply put, PBS will send signals by mocrowave from L'Enfant Plaza to the Bren Mar terminal. That terminal will send the signal to satellites owned by Western Union Corp. which will return the signals to the ground antennae of PBS stations. The stations then will be able to choose the programs they wich to broadcast to viewers.