You are 40 years old if you were born on February 29, 1984.
While someone born on a leap day only gets to celebrate an actual birthday every four years, their age still increases by one year with each passing year, just like everyone else. The common joke about leap year babies only being a fraction of their actual age refers to the number of times they've celebrated their birthday, not their actual age.
For instance, in 2024, someone born on February 29, 1984, would have reached their 40th year of life. However, they would have only experienced ten February 29th's in their lifetime to celebrate their "official" birthday.