What are the rising action, falling action, and resolution of "The Masque of the Red Death"?
There are several phases in a basic plot (known sometimes as Freytag's Pyramid). There's no hard and fast way of assigning parts of the story to each plot point, so what follows is simply my take. You only asked about three of these stages, but let's look at each stage one by one:
Exposition: setting the scene: Poe does this in the first paragraphs; inside the castle all is ease and beauty; outside all is death and pestilence.
Inciting incident: Prospero’s masquerade ball, and the incident of the Red Death. The problem the plot addresses might be “How to avoid getting this deadly disease,” or, “How to entertain oneself while in quarantine."
Rising action: In any event, the rising action curiously is not “action” at all, in my view, but the description of the rooms in the castle where the ball is held. Each of the rooms, associated with a dominant color, represent a kind of “state of mind” for Prospero, culminating in the terrifying black room with the red windows. As we progress through the rooms, the frenzied state of the reveling increases, punctuated by the tolling of the ebony clock, the mournful sound of which causes everyone to become unnaturally still.
Climax: The appearance, as the clock strikes midnight, of the masked figure of the Red Death.
Falling action: Prospero’s attempt to kill the masked figure.
Resolution: Prospero’s death in the velvet room. Ordinarily, the resolution is the “solving of the problem,” but here the problem, if we understand it as “how to stay alive,” is definitely NOT solved. If the problem is “how to cheat death,” then the resolution’s “solution” is simply that you can’t. If, on the other hand, the problem is how can one come to grips with one’s own insanity, the answer the resolution provides is a little different; Prospero’s progress through the rooms (which I think of as different sections of his mind), and his fury at the masked figure, gives him the courage to penetrate the darkest corner of his mind. His attempt to kill death is also an attempt to “kill” his insanity; the only “way out,” according to this reading, is to die himself.
Denouement: The realization that the masked figure is not a person at all, but death itself.
Edgar Allan Poe's allegorical story "The Masque of the Red Death" examines the spread of a dangerous disease ("the Red Death"), the symptoms of which are "sharp pains, and sudden dizziness, and then profuse bleeding at the pores, with dissolution," all of which lead to death within the space of half an hour. After a drop in the population, Prince Prospero gathers a thousand of his friends (all wealthy or titled individuals) to seclude themselves away from this terrible disease. After five or six months of seclusion, Prospero decides to throw a grand masquerade ball for his friends. They dance through the night while those outside the walls perish from the disease.
The rising action of this story occurs when the partygoers notice a man dressed as the Red Death, with "the countenance of a stiffened corpse." This generates "disapprobation and surprise" and then "terror...horror... disgust." Prince Prospero chases after the man with a dagger, but he falls dead before he can attack the man.
The falling action of this story is the death of the revelers "one by one" after they realize that the masked man is indeed the Red Death...the disease itself.
The resolution of this story is the triumph of death over all living things, with "...Darkness and Decay and the Red Death [holding] illimitable dominion over all." Despite their attempts to use their wealth and power to hide from the disease, all human beings are subject to death.
The rising action in the story is that the party is getting under way and everyone is forgetting about the world outside the castle that is suffering from the Red Death. The only reminder is when the ebony clock chimes ominously every hour.
The falling action is when the party goers realize that the uninvited guest who appears at midnight is in fact the Red Death himself and they all begin to die.
The resolution of the story is that no one can escape death no matter how fiercely they try to ignore it. The party goers tried to shut death out, but death will always find a way in when the time is right.