Federal officials have approved Prince George's County's request to establish a duty-free industrial area in Bowie, the first so-called foreign-trade zone in the Washington area.

County Executive Lawrence Hogan made an unusual appearance before the County Council yesterday to announce approval of the zone and used the occasion to do some bragging about his economic development efforts.

While the announcement was greeted enthusiastically, Hogan was subjected to some pointed questions about his recent trip at county expense to Europe. The trip was designed to interest foreign firms in the county.

Council members previously expressed concerns about the trip's cost, initially estimated at around $20,000, and yesterday they asked Hogan whether the expense was worth it to the county.

"I don't think it cost the $20,000 it was heralded to be," Hogan said, adding that he was "confident that in the long-term the foreign trade zone and . . . the European trip will be very beneficial to Prince George's.

Hogan has defended the European trip as an important part of his effort to attract foreign companies and the jobs and taxes they would provide to Prince George's.

The foregin-business effort is also an important part of what Hogan has said at various points is the keystone of his administration -- economic development. To that end, he has been traveling around the country lately to attend business conventions and host hospitality suites for businessmen. Just last week he returned from a Miami convention of corporate executives involved in finding locations for their companies to expand.

Hogan said yesterday that the foreign-trade zone, a concept he has been touting for the last year, would bring in hundreds of future jobs and possibly as much as $35 million in private investment in the next five to seven years. So far about 25 companies, both foreign and domestic, has expressed an interest in using the county's foreign-trade zone.

The zone will be a duty-free area located on 77 acres of county-owned land just south of Bowie. It will be used by any company that does some foreign business to import, assemble and test its foreign merchandise without paying the normal customs taxes. The duties are paid by the company only when the products leave the foreign-trade zone to be sold.

With the awarding of the trade-zone license this week, Prince George's becomes the only jurisdiction in Maryland and in what is called the District of Columbia port of entry to have received such approval. The county zone, when put into use sometime in 1981, will be the 63rd in the nation.