Each side of a square measures 65 m 5 dm.Find its area. By how many square metres does it fall short of a hectare?

To find the Area of a quadrilateral, you always multiply Length * Width. In the case of a square, all sides are the same length, so you simply multiply 65.5* 65.5. The reason you can use 65.5 is that there are 10 decimeters in one meter, so if you convert decimeters to meters you have 5/10 of a meter.

This is a two-step problem. After you have found the Area of the square, you must then subtract it from 10,000 which is how many square meters are in a hectare.

Your problem will look like this:

65.5*65.5 = A of square

10,000 - A = X sq meters

What are the themes of "The Namesake" and explain how they are significant to the title.

Identity: Gogol struggles throughout the novel with his dual identity - American and Bengali. He changes his name in an effort to do away with any negative connotation there is with the origin of his name. Nikolai Gogol was considered an eccentric man and Gogol Ganguli does not want to be associated with the weirdness of Gogol the author. However, he feels this way because he does not know the true origin of his namesake. This theme is relevant to the title because the namesake means different things to different people. Most people are indifferent towards the name Gogol. To Ashoke, it has a great significance because a) it is the name of his favorite Russian author and b) he was clutching a page from Nikolai Gogol's "The Overcoat" when he was pulled from the train wreck. To Gogol, it is not connected to him or his Bengali heritage in any way and therefore he initially rejects it.

Culture Clash: In an attempt to do things the Bengali way, Ashima and Ashoke take their kids to Bengali cultural events, read them Bengali literature and take them on trips to Calcutta. However, the Ganguli children quickly adopt the American way of doing things and their parents, in order to please their children, incorporate these traditions in the Ganguli home. The relevance of this theme to the title is that Gogol's name means nothing in this country but to his Bengali parents it has much significance. Gogol represents his Bengali side whereas Nikhil represents his American side. Hence, two name for one person further conveys this idea of cultures clashing.

What is the political situation in Scotland when Macbeth opens?

A war between the Scottish army and invading Norwegian troops reinforced by some Scottish rebels, led by Macdonwald and the Thane of Cawdor, is taking place. Macbeth and Banquo are the captains leading Duncan's forces. The outcome of the battles will determine Scotland's future. Will it continue to be a sovereign nation with Duncan as king, or will it fall to the invaders?

How is Dimmesdale the most tragic character in the book and one of Hawthorne's best psychological portraits? If not, then why is he not?

Dimmesdale is one of Hawthorne’s best psychological portraits in that Hawthorne allows us to glimpse Dimmedale’s inner life, and his struggle and rejection of that inner life. 

In rejecting his authentic inner experience in favor of the beliefs of the church fathers, Dimmesdale is the most tragic character in The Scarlet Letter. Unlike Hester, Dimmedale accepts the church fathers’ definition of adultery as a sin. 

Dimmesdale’s greater sin, however, is not adultery but that of denying himself a loving and sexual relationship with Hester.  If Dimmesdale had admitted his sexual relationship with Hester and had chosen to leave town with her, as she suggested, he would have found redemption in their relationship. After all, it is his relationship with Hester that evokes his passion, his spirituality, and makes him an effective preacher.  

Hawthorne describes Dimmesdale’s preaching voice like this: “This vocal organ was in itself a rich endowment;. . .  Like all other music, it breathed passion and pathos, and emotions high or tender, in a tongue native to the human heart.” Dimmesdale’s ability to connect with the human heart is a result of his connecting with his own heart through loving Hester.

Hester sees that Dimmesdale is denying his inner life and is suffering mentally and physically because of it. She confronts him saying, “Thou art crushed under this seven years’ of weight and misery. . . Exchange this false life of thine for a true one.”

As a result of this conversation with Hester, “His spirit rose as it were, with a bound, and attained a nearer prospect of the sky, than throughout all the misery which had kept him groveling on the earth. . .” Dimmesdale says, “Do I feel joy again?. . . O Hester, thou art my better angle! I seem to have flung myself-sick, sin-stained, and sorrow-blackened-down upon these forest-leaves, and to have risen up all made anew, with new powers to glorify Him that hath been merciful? This is already the better life!”

In the forest, Hester and Dimmesdale resurrect their love and Hawthorn provides us the following description about their love. “Such was the sympathy of Nature--that wild, heathen Nature of the forest, never subjugated by human law, nor illumined by higher truth--with the bliss of these two spirits! Love, whether newly born, or aroused from a deathlike slumber, must always create a sunshine, filling the heart so full of radiance, that it overflows upon the outward world.”

Hawthorn describes Dimmesdale’s insight in the forest with Hester like this, “Another man had returned out of the forest; a wiser one; one with a knowledge of hidden mysteries which the simplicity of the former never could have reached.”

Dimmesdale’s tragedy is that he lacks the courage to hold on to that new and wiser man, and to his new insight that Hester is his better angle. Instead of validating his own inner experience, Dimmedale allows himself to revert to the repressive beliefs held by the church fathers. In so choosing, he deserts Hester for the second time and dooms himself to a public and tragic death on the scaffold.

Post Script: Dimmesdale will not have died in vain if those of us living today learn from his tragedy by learning to respect our own inner experience and learning that a passionate, loving, sexual relationship is a path to a spiritual experience. When we can do that, we will have gained knowledge of the hidden mysteries.

In "A Separate Peace" what symbolic role does Finny's death play in the story?

Finny was a unique character who possessed a special quality of happiness and peace that many other characters strived to have, and failed.  Genes states of Finny,

"He possessed an extra vigor, a heightened confidence in himself, a serene capacity for affection which saved him...nothing...had broken his harmonious and natural unity."

Before this, Gene explained that most people came up against something in their lives that tested them to the max, and broke them, "and they were not the same again."  For most characters in this story, it was the war.  Once they realized that there was "this overwhelmingly hostile thing in the world with them," they broke, changing forever.  However, Finny didn't.  He remained himself.  So, at last, Gene states, he broke Finny.  So when Finny dies, it symbolizes how nothing is invincible; each of us will be changed by something in the world around us-a war, a trial, even a jealous friend-and we will have to surrender our peace to that change.  It is a dismal ending; Finny represented the ability to stay happy and separate from the brutal world around us, and when he dies, the last bit of peace fled with him.  Finny symbolized peace, harmony and innocence; his death symbolized the departure of that.  It is a "growing up", a surrender to the world, and the conquest of reality over innocence.

How is honesty the most prevalent theme in The Great Gatsby? Explain the importance of this theme and why it should take priority over two of...

In The Great Gatsby, honesty is a huge theme, as no one is quite what they seem.  Be it Tom who plays the devoted husband, yet leads Nick to his apartment in the city where he has an open affair with a girl from the Valley of Ashes, or Daisy who appears weak and defenseless, yet later on runs over her husband's mistress in Gatsby's car, characters are very multidimensional.

Gatsby refuses to give straight answers, and it is not until after he all but loses hope for achieving his goal of winning back Daisy that he comes close to being honest with Nick, the narrator.  In fact, Nick doesn't get the whole picture of Gatsby's life until after he is dead, and he has an opportunity to speak with his father, Mr. Gatz, at a very poorly attended funeral. 

No one is what they seem.  Jordan cheats at Golf, while Tom, Daisy, and Myrtle all have extramarital affairs.  When Nick tells Gatsby that he's worth "the whole damn lot of the put together", he is making a valid judgement call in that no one else ever comes clean and exhibits true honesty except for Gatsby in the end.  This adds a lot of meaning to the quote early on in the novel where Nick says, "No, Gatsby turned out alright in the end... it was what preyed on him" that finally got to him.

Why are Macbeth's first words, "So foul and fair a day I have not seen," important?

These words are important since they immediately introduce us to the theme of paradox and equivocation. Macbeth's statement engenders a clear contrast. Two conflicting ideas are expressed in the same sentence, 'foul' is the direct opposite of 'fair'. This is exactly the kinds of situations Macbeth will be confronted with throughout the play.

The evil sisters sisters, though, do not deem the two as contrasting ideas and treat them as equals. Their paradoxical statement, 'Fair is foul, and foul is fair' is an expression of their duplicity. They intentionally set out to deceive the gullible Macbeth and drive him to strive for ambition. In the process, he commits the most heinous of crimes. Ambition is a good thing and therefore fair. Macbeth's 'overriding ambition,' though, is malevolent and thus foul. Macbeth's desire to achieve the golden round turns him into a remorseless killer who spares no one.

It is not only the witches, though, who practice this kind of dastardly deception. Both Macbeth and Lady Macbeth actually encourage one another to be devious. She for example, tells her husband to 'look the innocent flower, but be the serpent underneath'. He, likewise, advises, 'false face must hide what the false heart doth know.' In both instances they urge one another to appear one way but in actual fact be the exact opposite. The appearance is fair, but the real intent is foul. They are remorseless in this and commit murder without batting an eyelid.

Throughout the play Macbeth commits the most heinous deeds which, to him, are fair measures to protect his position, even though he uses foul means to ensure his security. He has the innocent Banquo murdered and has Macduff's entire family slain because he sees the two men as threats to his status.

However, Macbeth soon realises that he had been misled by the witches' seemingly favourable prophesies. He believed, for example that he was invincible for the witches had told him that:

none of woman born shall harm Macbeth

and  

Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him.

Macbeth realizes his folly in both instances. Firstly, he is told by one of his messengers that Birnam Wood seems to be marching towards the castle. This was Malcolm's troops who had each cut a bough off a tree to camouflage their numbers. Secondly, when he is confronted by Macduff and he commands him to surrender since he is protected by a charm, Macduff tells him that he was not naturally born since he had been from his mother's womb, 'untimely ripped.'

It is then that Macbeth realizes that the game is up and that he had been a pawn in the scheming witches' hands. He refuses to surrender and is killed by Macduff. What had been fair to Macbeth had become foul in the most dramatic and tragic manner.