I have two questions that have been bothering me and I cannot figure them out for the life of me. I was really hoping someone would be able to help me. Thanks in advance.

1) You are given a equilateral triangle that represents an island. On all sides of this island are beaches. You want to live at the point that has the minimum sum of distances from all the sides. And the question is where would this point be?

2) You are given a circle and told that it is to represent a cherry pie. The pie is 6in long. You are asked if you cut this piece of pie at an angle of 37 degrees from the center and 3 in long. What will the area be of the crust of the piece of pie you just cut? See picture:

Shot at 2007-07-16

Thanks!

2. Whenever you have a circular sector,

These formulas are true:

(I)$\displaystyle \,A\,=\,\frac{1}{2}r^2\theta$

(II)$\displaystyle \,s\,=\,r\theta$

So using (I), we have:..$\displaystyle A\,=\,\frac{1}{2}(3)^2\,33$

Solve that to get..$\displaystyle A\,=\,148.5\,in.$

Well that isn't the area of the crust, but the whole slice of pie; maybe it can lead you somewhere.