What does the speaker's choice of words such as, vowed, settled, avenged, and impunity show about his emotional state

This question refers to the short story "The Cask of Amontillado", by Edgar Allan Poe. More specifically, it refers to the first paragraph, where the mentioned words can be found:

THE thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that gave utterance to a threat. At length I would be avenged; this was a point definitely, settled --but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.

Answer and Explanation:

The speaker's word choice reveals a lot about his emotional state. He is clearly angry for having been offended by Fortunato, even though he never reveals what the offense was. He has a vengeful feeling toward his "friend", and he is also clearly determined to not only carry out his revenge, but to also remain unpunished. We can also tell that, in spite of his anger, he is able to remain cold, speaking of his murderous decision in tranquil yet decisive tone.

the answer is

r ≈5.641

plug in the area of 100 yards into the equation

100=

divide each side by pi

≈ 31.8309=

take the square root of each side to find r

=r

r ≈5.641