What is the significance of the setting in Trifles?

The main importance of the setting in Susan Glaspell's play Trifles is that, in all three of the realms within which it is described, it possesses and provides the clues that provide the solution to the main problem.

The play's problem consists on the finding out of what exactly happened at the home of Minnie and John Wright the night when Minnie apparently murdered John. More precisely, the sheriff and district attorney at the scene of the crime want to know what was the timeline of events that could help explain the commission of the crime, itself. The use of the setting, and the elements of suspense applied to the narrative, bring out the solution quite effectively.

Using the realm of time, or the era where the setting takes place, Glaspell provides clues that may inspire the audience to put together possible scenarios. For example, the era in which this play takes place is one that features a male-dominated and somewhat chauvinistic society. In it, women are often considered as second-class citizens and their issues are considered, as the play's title says, as "trifles". Hence, Minnie Wright, as a victim of a man of such society, had more than enough reasons to implode and lose her mind to the point of killing him.

Using the regional realm, Glaspell also provides clues that lead to solving the case. In this case, the geographical realm is the country side; cold and isolated. Mrs. Hale is who connects mostly to this setting as she explains to both Mrs. Peters and the county attorney how hard it is to be a farmer's wife; she talks about the cold winters, the lonely hours, the hard work, and the want for company in those endless days. This certainly provides further evidence as to what was Minnie Wright's state of mind at the time of the crime. 

Finally, using the realm of domain, Glaspell takes us into the heart of the action: the kitchen, as the woman's own, personal queendom. It is precisely throughout the kitchen that most of the state of mind of Minnie Wright is evident: the exploded compotes of fruit, the state of general dinginess, the decay, and the carelessness that would have made an otherwise-healthy country wife cringe. However, Minnie Wright was obviously in a terrified and stressful state of mind that led her to do everything, from cooking to stitching, in a state of complete chaos.

Therefore, Trifles is unique in that it provides all the clues right there in the main setting of the one-act play, making the delivery of the narrative essential to discover the hidden clues and subtle messages.

What is the significance of the farmhouse setting in Trifles and how does it reflect on the characters' personalities?

The setting of Susan Glaspell's play Trifles is a lonely farmhouse, and that setting does indeed have plenty of significance both for the plot and the characters. Let's look at some points you might mention as you construct your answer.

First, think about how the farmhouse represents isolation for Minnie Wright. She was cut off from society. Hardly anyone came to visit. Her husband was not sociable, and he never encouraged visitors. The isolation suited him just fine. But it did not suit Minnie. When she was the young Minnie Foster, she was a cheerful girl who got involved in community activities and had friends. After her marriage, that all stopped. The farmhouse became her whole life, and it was not much of a life.

Second, you should consider the clues that the farmhouse presents about what happened between Minnie and John Wright. Mrs. Peters and Mrs. Hale recognize and interpret these clues. They see Minnie's agitation in the way her kitchen looks. They understand her unhappiness. They recognize a woman doing her best in a miserable condition. Minnie cared about her home. That is evident from her concern about her preserves. But she apparently could no longer tolerate her life in that lonely farmhouse.