The Federal Reserve Board has approved the proposed merger of First Virginia Bank, based in Falls Church, and Farmers and Merchants State Bank of Fredericksburg, First Virginia said yesterday.

The merger, which is scheduled to take effect about June 1, will create a new bank with assets of $850 million and 73 branches covering a triangle from Arlington to Fredericksburg to Warrenton.

It is the latest in a wave of mergers and acquisitions that are changing the corporate structure of banking across Virginia. Early last month, the state's largest and fourth-largest institutions, United Virginia Bankshares Inc. and Dominion Bankshares Corp., announced that they are "exploring the feasibility of an affiliation."

Less than two weeks before that, the state's second-largest bank, Virginia National, and the fifth-largest, First & Merchants, agreed to combine.

Thomas Jennings, First Virginia's general counsel, said his bank's shareholders have approved the merger with Farmers and Merchants. Stockholders of the Fredericksburg bank are scheduled to vote on April 18.

Both banks are state-chartered institutions regulated by the Federal Reserve Board. The U.S. Department of Justice has 30 days from the date of Federal Reserve action to review the proposed merger for possible antitrust implications, but Jennings said he does not anticipate any hitches.

After the merger takes effect, existing branches of Farmers and Merchants will become branches of First Virginia. The overall size of First Virginia's parent 21-bank holding company will grow to $2.1 billion in assets, a bank spokesman said.