Chapter 2 of Nathaniel Hawthorne's classic, The Scarlet Letter,is titled "The Market-Place" introduces us to a newly-freed Hester Prynne leaving the prison. She is holding Pearl who is an infant of around 3 months old. Hester suffers the humiliation of being escorted out of jail holding a child that was obviously born behind bars. This, she did under the watchful eye of the hypocritical society of the settlement.
She bore in her arms a child, a baby of some three months old, who winked and turned aside its little face from the too vivid light of day; because its existence, heretofore, had brought it acquainted only with the grey twilight of a dungeon, or other darksome apartment of the prison.
Meanwhile, as time passes and Arthur Dimmesdale elects to confess his sin at the scaffold he is holding an older Pearl. Dimmesdale did not die of an old age; he had been psychologically mortified for so long that he died of the effects of sustained nervous wreck.
We know that Pearl is seven years old when Dimmesdale dies, and that Dimmesdale is a relatively young man. In fact, he is the youngest of the elders in the settlement It is his youth and dedication to God which earns him the admiration of the settlement.
The aged members of his flock, beholding Mr. Dimmesdale's frame so feeble, while they themselves so rugged in their infirmity, believed that he would go heavenward before them, and enjoined it upon their children that their old bones should be buried close to their young pastor's holy grave.
Therefore, judging that Dimmesdale's punishment begins when Pearl is born and ends when she is seven years old, we could ascertain that Dimmesdale was barely older than Hester, who at the time of their affair was still in her 20's. Hence, we can conclude that Dimmesdale died in his early 30's. This, would have been considered a rather mature age but, for a clergyman, it was considered still quite young.