As a home builder in Hampton Roads, Helen E. Dragas has won praise for solving big problems decisively. Several years ago, she learned that a subcontractor her business hired had been using defective drywall that emitted an odor and raised concerns about wiring corrosion and health. Dragas decided to relocate people, tear out the drywall and rebuild more than 70 houses.

“She did not have to be threatened. She did not have to be taken to court,” said former Virginia Beach mayor Meyera Oberndorf. “She just immediately made it right at her own expense.”

But as rector of the University of Virginia’s governing board, Dragas has been vilified for orchestrating the removal of a president who she thought wasn’t moving fast enough to solve big problems. How Dragas handled the ouster of Teresa Sullivan — a surprise action, without a vote from the full board of visitors — confounds many who know her.

“Helen has always had the reputation of being bright. She runs a good business and is a good citizen,” said Jane Batten, a major donor to U-Va. who lives in Virginia Beach. “I’m surprised at her lapse in judgment in this matter.”

These portraits of Dragas the business leader (smart, tough and generous, admirers say) and Dragas the university leader (secretive, unilateral and divisive, according to critics) conflict so sharply that they are difficult to reconcile. The common thread may lie in a quality her allies often invoke: her resolve.

In recent days, protesters have massed on the university’s historic Lawn in front of Thomas Jefferson’s Rotunda. Newspaper editorials have demanded answers. Donors have threatened to withhold funds. Faculty have called for Dragas to step down.

“I’ve never seen one person have such a negative impact on a large institution like this,” Elizabeth Friberg, a nursing professor, said at a rally in Charlottesville on Wednesday. “Maybe there were two. Maybe there were three. But she’s the face of it, and she’ll have to live with that.”

Dragas has not retreated. She issued a statement of regret Monday for missteps that contributed to the upheaval but defended the need for the board to make “important and often difficult calls.” She held her ground even as one of her board allies resigned.

On Thursday, the board set a meeting for next week to discuss whether Sullivan should be reinstated — a possibility that her supporters say she would consider if Dragas resigned.

Dragas’s term on the board ends July 1. She is eligible for reappointment and has not indicated in public any desire to leave. Gov. Robert F. McDonnell (R) will make the call.

On Tuesday, he said of her: “From all accounts, she has been an incredibly good leader and strong participant on the board in helping to manage the university.” But the governor has not tipped his hand on whether he’ll keep Dragas.

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Dragas, 50, is president and chief executive of the Dragas Cos., a family business dating back more than 40 years that builds condominium communities and moderately priced homes.

Her father, George Dragas Jr., traveled with his family to Greece for a visit when he was a little boy and could not get home because of the onset of World War II. They were stranded in Nazi-occupied Athens with relatives, often going hungry.

“My husband’s experience in Greece definitely shaped his life, and I’m sure those values have been handed down to our children,” Helen Dragas’s mother, Grace Dragas, wrote in an e-mail. “The dire circumstances they faced gave them a steely resolve and a fighting spirit, and a real commitment to family.”

Helen Dragas grew up with the business — she started when she was 13 with a summer job there and has never worked anywhere else. She returned after graduating from U-Va. in 1984 and again after earning her master’s in business administration in Charlottesville in 1998.

She rose to head of the Dragas Cos. in 1996. Dragas is married with three children.

Development in Virginia Beach can be controversial, Mayor William D. Sessoms Jr. said. But he said Dragas is respected and well-liked in the area. “She goes in and meets with the community, works with the community and comes up with a plan the community can support. . . . She’s analytical. She thinks before she speaks.”

Over the years, Dragas has served on a number of powerful public and private boards and has donated to candidates from both parties. Records tracked by the nonpartisan Virginia Public Access Project show that Dragas and entities related to her business have donated more than $70,000 to political campaigns since 1999, mostly to Democrats. She forged ties with Gov. Mark R. Warner (D) and his successor, Democrat Timothy M. Kaine, who named her to the U-Va. board in 2008. In 2010, the board named Dragas vice rector as she turned back a challenge from another board member. In 2011, she became U-Va.’s first female rector, the year after Sullivan became its first female president.

George Dragas was also a rector, leading the board of visitors of Old Dominion University in the early 1990s. Last week, while Helen Dragas was in Charlottesville, relatives were at ODU for the dedication of a building named in their honor.

The Dragas Cos. recently donated $1.5 million to help the homeless in three cities in the Hampton Roads region, and Helen Dragas has been honored by Habitat for Humanity and other organizations. She is known in her home town as a civic leader.

But on Wednesday, she lost the support of her local paper.

“Helen Dragas, rector of the University of Virginia, has failed repeatedly to explain why President Teresa Sullivan was forced out a week ago,” the Virginian-Pilot said in an editorial. “Dragas has, however, built a convincing case for another departure — her own.”

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Dragas declined to be interviewed for this article. On Thursday evening, Dragas issued a statement saying that she agreed with critics who said the dismissal could have been handled better. But she reiterated her defense of the decision.

“In my view, we did the right thing, the wrong way,” Dragas said. “For this, I sincerely apologize, and this and future boards will learn from our mistakes.”

Dragas also listed challenges facing the university, including financial pressures and the emerging role of online learning, and said the board concluded that there was a need for a rapid development of a new strategic plan.

Some e-mails, released by the university after a public records request from the Cavalier Daily student newspaper, hint at Dragas’s management style.

On June 7, Dragas wrote to Sullivan: “Terry, [Vice Rector] Mark [Kington] and I will both be in Charlottesville tomorrow afternoon and would appreciate a meeting with you. Are you free sometime after 3 pm? Thank you, Helen.”

Sullivan replied that she would be free by 5 and asked, “Is there anything you would like me to prepare?”

At that meeting, Dragas and Kington told Sullivan that they had the votes on the board to force her out.

On June 10, Sullivan resigned and a firestorm erupted.

On June 14, according to an e-mail obtained by The Washington Post, Dragas told the provost and the chief operating officer that she and the vice rector wanted them to issue a joint statement by noon. They should tell the faculty and staff, she wrote, that they would support future U-Va. presidents and make clear “that you understand that the [board’s] action is authoritative and resolute.”

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At nearly 3 a.m. Tuesday, Dragas left the Rotunda after a marathon board meeting. She was shepherded by a police escort past students who shouted “Shame!” and “Resign!” She didn’t answer questions. She had already spoken her piece, a prepared statement read many hours earlier.

It had taken more than 11 hours, but Dragas had gotten the result she wanted, overriding board members who fought to reinstate Sullivan. The board had chosen an interim president, commerce school dean Carl P. Zeithaml. She was pushing ahead.

“She’s very considered and careful and deliberate in her thought process,” said Philip Shucet, a friend and former head of the Virginia Department of Transportation. “She made her decision and is now about the business of moving forward. That’s very Helen.”

In an interview with Virginia Business magazine, published in March, Dragas said: “The academic environment is one of shared governance, which is quite different than running a for-profit company. I recognize that, and I try to honor that.”

As for her management style, she said, “I would say I set high standards, but I put a lot of thought and energy into hiring the right people.”

Staff writers Daniel de Vise in Charlottesville and Anita Kumar in Richmond contributed to this report.