The Zoning Board of Appeal on Tuesday approved a land owner's plans to replace a convenience store and a parking lot on its land at 1420 Dorchester Ave., near Adams Street, with a five-story, 46-unit apartment building.

The Gordon family, which owns the lot, had originally proposed a four-story building, but added an extra floor after some nearby residents actually said they wanted to see more apartments in the area, the family's attorney, George Morancy, told the board.

Morancy said seven of the apartments, or 15% of the total, would be rented as affordable, to people making no more than 70% of the Boston area median income.

The building would have 33 parking spaces in an underground garage as well as groundfloor commercial space.

Residents would get a rear private greenspace - which would also serve as a buffer for homes in the rear - as well as a public plaza with some artwork along Dorchester Avenue.

The building's exterior is full of "architectural richness," Mike DelleFave of RODE Architects said "No sides are cheapened."

The proposal needed zoning-board approval because it was taller and bigger than otherwise allowed and did not have as many parking spaces as it otherwise would have needed. The BPDA board approved the project in December. It also needed approval because five of the apartments would be on the ground floor, although DelleFave said that because of the topography of the lot, the units are actually several feet above ground level.

1420 Dorchester Ave. filings.