ShmoopTube

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And here's your shmoop du jour.

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Suppose a square with a side, s, is inscribed in a circle.

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The area, in terms of s, outside of the square but inside of the circle is given by the following graph.

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What is the approximate area of this region if the square has a perimeter of 32?

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Here are the potential answers...

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Before we spoil the ending, hit pause and try this one yourself.

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OK, this is a multi-parter; we have to remember

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the formula for the perimeter of a square...

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...and then we have to be able to read a graph with this curvy line thingy.

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First off, a square got its name because it means that all 4 sides are equal.

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So if the TOTAL perimeter is 32, and there are 4 sides...

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...what's 32 divided by 4?

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That's right... each side has a length of 8.

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And ooh, curveball -- note that one of the answers is 8. But beware... that 8 is only

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the distance of one side of the squares.

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And knowing that fact is a big part of the question.

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Like... if we didn't know how to make that initial fancy drawing in the beginning, we'd be in real trouble.

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Now we have to apply that 8 unit distance to the graph.

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And if we start here and move straight upwards until we hit the curve, we hit it here...

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...and come straight left to hit the y axis here. So where is... here?

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Well, note that this line is half way between 48 and 0 so it's gotta be 24.

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And our line hits half way between the 24 and the 48 so that line hits 36.

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The answer is C.

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Don't worry, we won't forget to invite you to the briss.

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