Grocery prices in the Washington area rose by 2.2 percent during August, following a three-month period in which food prices rose by 7.4 percent, the government said yesterday.During the first five months of 1980, grocery prices rose by only 1.9 percent.

The 2.2 percent unadjusted food price hike in theis area compares with a 1.9 percent increase in grocery store prices across the country and tops the 2.0 percent rise in area food prices during July.

Some retail food experts expect to see metropolitan-area price increases moderate in light of the emergence this summer of cut-rate and box food stores. mThe August figures do not yeat reflect the development of these new factors in the local grocery picture.

But one government analyst pointed out that the Washington area has not felt the effects completely of the long drought across major sections of the nation's agricultural belt. Even though the price of meat and related farm products rose during August, further increases may be expected this fall.

Although the increase in the price of fruits and vegetables dropped from a record high of 10.2 percent in June to only 0.8 percent in August, sharp increases in the price of meat, poultry, fish and eggs led the local price rise, according to figures compiled by the Bureau of Labor Statistics.

In fact, the 3.8 percent August increase in the price of meats and related products topped the 3.7 percent increase in those same grocery goods across the nation, according to the government figures. During July, the price of meats, poultry, fish and eggs rose by 2.9 percent in the Washington area.

On the other hand, the price of cereal and bakery products dropped by 0.3 percent in August after rising by 0.8 percent during July. Cereal and bakery product prices rose by 0.6 percent across the country during August.

Diary prices rose by 1.1 percent in August after going up by 1.4 percent in July. Across the country, dairy prices rose by only 0.5 percent.

In other categories, food prices rose dramatically here. During August, prices rose for most fresh fruit and pork items.