To the loud approval of a crowd of more than 1,200 Fort Hunt High School students and parents, the Fairfax County School Board decided last night to repair and reopen the burned out school rather than close it forever.

The thunderous applause that greeted the board's 7-to-3 vote reflected the concern that Fort Hunt parents and students had felt at the possibility that their school might be eliminated because of falling enrollment. The joy was undiminished by the fact that the board may vote next week to restore the school, heavily damaged by arson Dec. 29, at smaller than its present size.

"You would have to go a long way to find somebody unhappy about this," said Fort Hunt guidance counselor Robert Walden. "We can all feel very heartened."

Two 13-year-old Fort Hunt seniors and a 19-year-old graduate have been charged in connection with arson that caused an estimated $4.5 million worth of damage to the school.

Fort Hunt parents had organized a broad coalition to light to keep the school open, seving that they would use all "reasonable and leavel" methods to change any decision to close the school.

School Superintendent S. John Davis said last week he hoped a portion of the school would be ready for occupancy by May 1 and at the latest by September.

The board deelined to act last night on Davis' recommendation that the school be rebuilt to hold only 1,500 students rather than the 2,000 students it can now hold. The board is expected to decide on Thursday what size to rebuild the school. Enrollment projections show that if the school were built to hold 1,500 students, it would be overcrowded until 1983 when enrollment would drop to about 1,480.

Davis said he recommended reopening Ofrt Hunt because of potential disruptions at other schools to which its students might have transferred and because closing Fort Hunt would limit classroom space in that area of the county if students at other high schools must be moved to relieve overcrowding.

The board now must decided how to rebuild the school. Insurance payments for damage to the school may be reduced if the board attempts to combine $2.3 million worth of improvements -- approved in a bond referendum last year -- with the restoration project.

Davis also recommended that the students displaced by the fire remain at Groveton High until March 23. They would then be transferred to Mount Vernon High on the same double shift basis on which they are attending Groveton.