The Zoning Board of Appeal last week approved a landowner’s plans to replace a Richdale convenience store and a parking lot at 1420 Dorchester Ave near Adams Street, with a 5-story, 46-unit apartment building.

The BPDA board approved the project last December.

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

Seven of the apartments, or 15 percent of the total, will be rented as affordable to people making no more than 70 percent of the Boston area median income, the attorney said.

The building will have 33 parking spaces in an underground garage as well as ground-floor commercial space. Residents will have a private greenspace in the rear, which will also serve as a buffer for homes in the area - 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 proposes something taller and bigger than otherwise allowed and does not have as many parking spaces as it otherwise would have needed. 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.