Kara Kennedy, the daughter of Senator Edward M. Kennedy of Massachusetts, died Friday after a workout at a Washington-area health club. She was 51. The cause was a heart attack, according to the Edward M. Kennedy Institute for the United States Senate in Boston, which announced the death.

Her brother Patrick J. Kennedy, a former Rhode Island congressman, said, “She’s with my dad now, that’s a consolation for all of us.”

Ms. Kennedy became yet another member of America’s most famous political family that, across two generations, has either died young or relatively young. In her generation alone, John F. Kennedy Jr. was killed in a plane crash in 1999; Michael L. Kennedy died in a skiing accident in 1998 and his brother David of a drug overdose in 1984. Edward Kennedy died of brain cancer in August 2009 at the age of 77, the only one of four sons to survive to old age.

Ms. Kennedy, a filmmaker and the eldest of the three children of Mr. Kennedy and Joan Bennett Kennedy, was a shy person and led a more private life than most of the grandchildren of Joseph P. Kennedy and Rose Fitzgerald Kennedy. In an article she wrote for The Boston Globe Magazine in April on the Kennedy Institute’s coming groundbreaking, she said: “Unlike my father, I felt more comfortable behind the camera than in front of it. But like him, I found my greatest fulfillment in showing the needs and successes of others.”

In his 2009 autobiography, “True Compass: a Memoir,” Mr. Kennedy described his daughter’s struggle with lung cancer. When she first received the diagnosis in 2002, it was described by doctors as inoperable. But the family, Mr. Kennedy wrote, “refused to accept this.” They found surgeons who were willing to treat her. The cancer went into remission.

Kara Anne Kennedy was born on Feb. 27, 1960. She graduated from Tufts University and went on to a career in television and film. She produced a film for the institute’s inaugural gala, as well as several videos for Very Special Arts, an organization for people with disabilities, which was founded by her aunt Jean Kennedy Smith. Until 1990, she was a producer of “Evening Magazine” on WBZ-TV in Boston.

She served on the national advisory board for the National Organization on Fetal Alcohol Syndrome and was a director emeritus of the John F. Kennedy Presidential Library and Museum.

In 1990, she married Michael Allen, a member of the United States sailing team that won the Sardinia Cup in 1980. They had a son, Max, and a daughter, Grace.

They survive her, as do her mother; her brothers, Patrick and Edward M. Kennedy Jr.; her stepmother, Victoria Reggie Kennedy; and her stepbrother and stepsister, Curran and Caroline Raclin.

Patrick Kennedy said of Max and Grace, “The best way for us to think about Kara is to think about them because they were the most important thing in her whole life.”