Washington-area school systems could lose as much as $43 million in federal aid for the coming school year if President Reagan's package of budget cuts is approved, school officials said yesterday.

The federal fund reductions in such programs as subsidized lunches, impact aid and vocational education come at a time when most area school systems are already being pinched by municipal cash shortages.

Declining enrollments are forcing school boards to close dozens of neighborhood schools. Soaring energy costs are sending already lean school budgets into the red. Teachers in the District and Maryland are being laid off or clamoring for salary increases.

If Reagan's proposals are adopted by Congress, the already financially strapped school systems would face even greater problems, area administrators said yesterday.

The Reagan cuts have been criticized as being aimed primarily at the poor. But the reductions would have far-reaching and critical impact on nearly all of the school systems in the Washington area -- from affluent Montgomery and Fairfax counties, where municipal service burdens are lightest, to Prince George's County and the District of Columbia, where burdens are heaviest:

D.C. schools, which already are facing a $10 million deficit in next year's budget, would lose an additional $13 million in federal grants. Officials said that would lead to an increase in class sizes from 28 to 30 students, elimination of vocational education programs in junior high schools, drastic reductions in special reading and mathematics programs for the economically disadvantaged, higher costs for lunches and possible elimination of the school breakfast program.

Fairfax County schools would lose $15.3 million in federal grants, including money for school lunches, vocational and adult education programs and programs for the handicapped. More than half of the $15.3 million loss would be impact aid -- federal funds sent to municipalities that provide services to areas with high concentrations of federal employes and facilities. Impact aid has become a key supplement in many municipal budgets here.

Prince George's County school officials anticipate losing $9 million, leading to a 20 percent reduction in the county's vocational education programs as well as a major cutback in the number of pupils eligible for free or reduced-price lunches. Currently, 25 percent of the county's 121,800 public school students are eligible for the subsidized lunch program.

Montgomery officials expect to lose at least $2.4 million in impact aid, but have yet to determine the full extent of the proposed cuts.

Arlington faces a loss of $2 million in impact aid and funds for special reading and mathematics programs. School officials hope to recoup some of the lost funds from the county government. But county officials have already indicated their intention to hold down school spending because of declining enrollments.

In Alexandria, $1.1 million could be lost, including special education and lunch program funds as well as impact aid funds. School officials are uncertain about other sources of funds.

"If [these funds are cut] can public education continue to carry out its mission for this city?" asked D.C. board president Eugene Kinlow (At-large), testifying yesterday before the House District Appropriations Subcommittee on the school system's proposed $248 million budget for 1982.

"This is the time for the federal government to become part of the answer, not part of the problem," Kinlow said.

Bill Leonard, Alexandria's assistant superintendent for finance, said in an interview, "If the losses should be substantial, we would be forced to go back to the drawing board to determine what programs or services could be reduced."

Reagan has asked Congress to slice $4.7 billion from former president Jimmy Carter's funding requests for the Department of Education for the fiscal year beginning Oct. 1 and includes the 1981-82 school year.

Congress has just begun to consider the proposals, but Reagan suffered an early setback Tuesday when the House Education and Labor Committee rejected every one of the proposed cuts in programs that fell under its jurisdiction.

That committee is one of the most liberal in Congress, however, and the ultimate fate of the proposals is far from clear, observers say, especially with much of Congress in a budget-cutting mood.

The Reagan cuts were discussed yesterday on Capitol Hill when D.C. school officials appeared before the House District Appropriations subcommittee to testify on the city's proposed operating budget for the 1982 fiscal year.

Noting that the city has started new programs to raise standards and student achievement in Washington's troubled schools, Acting Superintendent James T. Guines said, "If urban education can be saved, [the District] would be a laboratory to demonstrate where it can be done. . . But at some point creativity and innovation run out and there is a need for [financial] resources."

School officials said they would need a budget of $258 million just to keep the same number of employes and programs next year that currently exist. The mayor and City Council have approved a budget of only $248 million for the 1981-82 school year.

The school system also faces a $6 million deficit in the current school year's budget because of cost overruns in fuel, electricity and transportation for the handicapped, and is requesting supplemental aid from Congress just to finish out this year in the black.

If the House and Senate committees are not forthcoming with further funds, the school system then would be forced to lay off either more employes or put employes on furlough, said board member R. Calvin Lockridge, chairman of the schools' finance committee. A furlough of all employes would save $1 million a day, Lockridge said.

The proposed Reagan budget cuts could force the school system to eliminate the practice of picking up handicapped students at home for busing to school. Instead, the students would have to be brought to various pickup points by family or friends, Lockridge said.

The cost of school lunches in D.C. public schools has already been increased to 45 cents a meal in elementary schools and 60 cents in secondary schools. A reduction in child nutrition funds as proposed by Reagan could price the meals out of the range of many poor families, school officials said.

Fairfax County would lose $4.5 million in meal subsidy funds -- 72 percent of the county's entire food-subsidy allotment, according to school officials. Such a reduction could lead the county to drop out of the federal program, according to one school official.

A Prince George's County official said the loss of federal school lunch and vocational funds would be especially difficult to absorb because of a charter amendment approved in 1978 that limits the amount of money the county can collect in property taxes.