Melody

The area of the whole square is 36

the area of tone quadrant =  \(0.25 \pi r^2= 0.25*\pi*(2\sqrt3)^2=3\pi\;\;cm^2\)

Let the bottom of this diagram be the x- axis. 

and  (0,0) is at the bottom left corner then the equation of the bottom left quadrant is 

\(x^2+y^2=12\\ y^2=12-x^2\\ y=\sqrt{12-x^2}\)

The area of the blue/ green overlap is

\(A=\displaystyle 2\int_3^{2\sqrt3}\;\;\sqrt{12-x^2}\;\;dx\\ =2\left[ 0.5x\sqrt{12-x^2}+6 * asin(\frac{x}{2\sqrt3} ) \right]_3^{2\sqrt3} \qquad \text{Wolfram|Alpha}\\ =2\left[ 0.5(2\sqrt3)\sqrt{0}+6 * asin(1 ) \right]-2\left[ 1.5\sqrt{3}+6 * asin(\frac{3}{2\sqrt3} ) \right]\\ =2\left[ 6 * \frac{\pi}{2} \right]-2\left[ 1.5\sqrt{3}+6 * asin(\frac{\sqrt3}{2} ) \right]\\ =6\pi-2\left[ 1.5\sqrt{3}+6 * \frac{\pi}{3} ) \right]\\ =6\pi-2\left[ 1.5\sqrt{3}+2\pi ) \right]\\ =6\pi-3\sqrt{3}-4\pi \\ =2\pi-3\sqrt3\)

So the desired area in the middle is

\(middle \;area =36-[\pi*(2\sqrt3)^2-4*(2\pi-3\sqrt3)]\\ middle \;area =36-[12\pi-8\pi+12\sqrt3)]\\ middle \;area =36-[4\pi+12\sqrt3)]\\ middle \;area =36-12\sqrt3-4\pi \;\;cm^2\\ middle \;area \approx 2.65 cm^2\\\)

You need to give us more information - an example to work with.

Try graphing both you graphs here.

Thanks Heureka, I did not know how to do that :)

Yes, it seems all polygons are circles in disguise :)

What a great discovery you have made   

The X-axis is the perpendicular bisector of the line segment joining the points (3,12) & (x,y). Find (x,y). 

Perpendicular means at right angles.

Bisector means cuts exactly in half.

Here is the pic :)

Mmm

Well I could see that the key numbers were going to be 2 and 16  can you see why?

I actually draw a rough number line and marked 2 and 16 on it.  Then I had to work out each of the 3 sections seperately.

for instance.  

try x=0     x-2=-2   so  |x-2|  must be  -(x-2) which is 2-x        at x=0 x-16 is already positive so  |x-16|=x-16

So when x is less than 2   the value will  be  2-x   +  x-16  etc.

Do you understand that?

You just need to think about that for each of the 3 sections of the graph and you will have your full answer.

Try drawing it on a rough graph. You should be able to see the answer easily.

I think that this is what you mean

 f(x)=|x−2|+|x−16|

When x is less then 2 then  x-2 and x-16  will both be negative SO

f(x)= 2-x+16-x = 18-2x

When x is between 2 and 16  x-2 will be positive and x-16 will be negative SO

f(x)=x-2+16-x = 14

When x is greater than 16   both expressions will be positive   SO

f(x)=x-2+x-16 = 2x-18

240 up to sea level then  8000 feet higher still.

You can do the addition!  :)