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CAHSEE Math 2.4 Algebra and Functions 194 Views


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Description:

Algebra and Functions Drill 2, Problem 4. What is the approximate area of this region if the square has a perimeter of 32?

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Transcript

00:03

And here's your shmoop du jour.

00:06

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

00:11

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

00:17

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

00:22

Here are the potential answers...

00:24

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

00:29

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

00:32

the formula for the perimeter of a square...

00:34

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

00:39

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

00:48

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

00:52

...what's 32 divided by 4?

00:55

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

00:58

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

01:03

the distance of one side of the squares.

01:06

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

01:08

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

01:15

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

01:19

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

01:24

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

01:29

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

01:35

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

01:40

The answer is C.

01:41

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

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