A pair of pricey luxury apartment buildings with ground-floor retail space will rise on an odd-shaped lot in Tribeca thanks to a city variance granted to the developer that will make the site more manageable to build on.

High-end builder DDG will erect two contiguous buildings, six- and eight-stories tall, on a parking lot at 100 Franklin Street that the firm purchased in 2014 for about $11.5 million. The buildings will have a total of about 30,000 square feet.

DDG received permission from the city’s Board of Standards and Appeals, granting it the ability to utilize the full size of the lot without having to set back the buildings’ upper floors from the sidewalk, which is required by the site’s zoning, but is difficult given their slender forms.

DDG purchased the site, a parking lot in the shape of two contiguous triangles that spans the entire block between Franklin and White streets along Sixth Avenue, knowing it would be tricky to build on.

“It’s a very thin lot but we immediately saw the incredible value of the over-200-feet of retail frontage it will have on Sixth Avenue and the site dimensions provide for unbeatable natural lighting to all residences,” said Joseph A. McMillan, Jr., Chairman and CEO of DDG. “There is a lot more demand for luxury retail in Tribeca and this is the kind of space that will appeal to both high-end restaurant tenants and fashion tenants.”

Although the retail space helped convince Mr. McMillan to buy the site, he has high expectations for the 10 luxury apartments he is building upstairs. DDG plans to seek at least $3,000 per square foot for the condos—a premium price that has become common in Tribeca.

2014_DDG Foundation_Render 1 CROPPEDAs part of the project, the charitable arm of DDG, known as the DDG Foundation, is providing funds to turn the pedestrian island formed by the intersection of Sixth Avenue and Church Street, across the street from the project, into a small plaza.

“It will be a place that anyone in the neighborhood, including residents of the building and passersby, can enjoy,” Mr. McMillan said.

DDG is designing and developing the buildings, as it has done with several of its previous projects. The firm plans to break ground on 100 Franklin Street by the fall and finish it in 2017.

The company is in the midst of erecting other residential buildings in the city. It is raising a 521-foot-tall condo tower on the Upper East Side at 180 East 88th Street, and it is getting ready to break ground on another condo project in Chelsea at 532 West 20th Street. DDG is also working on another Tribeca project at 12 Warren and 325 West Broadway, called XOCO 325 in Soho.