In the opening chapter of Harper Lee's To Kill a Mockingbird, we are told of the story of Arthur (Boo) Radley's house arrest and of his subsequent attack on his father at the age of 33. We can use that information to estimate Arthur's current age.
Scout informs us that Arthur was placed under house arrest by his father when he and some other boys got into trouble at the age of 18. The boys were convicted on multiple charges, and all but Arthur, as punishment, were sent to "industrial school and received the best secondary education to be had in the state" (Chapter 1). Mr. Radley refused to allow Arthur to be sent to the industrial school, thinking instead Arthur was best kept in Mr. Radley's own care. The Radley house then became completely shut up, and Arthur was not permitted to leave his house.
Later, it is said Arthur drove a pair of scissors into his father's leg as he passed by when Arthur was working on his scrapbook. Scout informs us Arthur was "thirty-three years old then" (Chapter 1). We also know Jem is nine years old at the start of the story, and Scout says that the incident of Mrs. Radley running screaming from the house after the scissor event is "barely within Jem's memory" (Chapter 1). It is at about the age of two to four years old that earliest childhood memories can be recalled. This means that five to seven years have passed since the scissor incident; therefore, Arthur is approximately 38 to 40 years old.