Six Washington-area rental housing projects are winners in an unusual high-stakes lottery conducted by the Department of Housing and Urban Development.

The lottery system was used to dole out the last of HUD's low-interest-loan money for low-income housing construction under the so-called Ginnie Mae Tandem program administered by the Government National Mortgage Association. For details see E4.

Of 769 projects nationwide that applied for part of the last $1 billion in funds, 246 were selected. Arlington County beat the long-shot odds by gaining funding for three of four projects submitted.

The Washington area has depended almost entirely on the Ginnie Mae Tandem program in the past few years for construction of severely needed rental housing. The program provides 7 1/2 percent financing for construction and rehabilitation of low-income, federally subsidized Section 8 housing.

The Reagan administration plans to end all Section 8 construction and the Tandem program, and is counting on savings from previously approved projects that cannot be built. Some will not be built because of the end of the Tandem funds.

Those in this area gaining funds from the lottery include:

A 123-unit new construction project on 14th Street between Fairmont and Girard streets on a city-awarded site.

The 133-unit Carmel Plaza North project in the District.

The last 48-unit phase of Cinnamon Run in Wheaton.

A 72-unit tenant cooperative at Arlington's Colonial Village. Another phase of the project did not win funding, however.

The 37-unit Knightsbridge project off Glebe Road in Arlington.

The 77-unit Arlington View Terrace in south Arlington.

Another $1 billion in Tandem funds was allocated to priority projects before the lottery. Here these included Atlantic Gardens in Southeast, the Covington cooperative on Columbia Road and the 600-unit South Laurel project, formerly Pumpkin Hill.

The large Benning Heights rehabilitation planned in the District lost out in the lottery. While other unfunded projects may turn to tax-exempt financing from local governments, the Benning Heights project is not eligible for this funding and probably will not be able to proceed.