<PRE><B>Question 1097200</B>
&lt;br&gt;I ONLY NEED TO KNOW PART C&lt;br&gt;
But your answers for parts A and B are not right....&lt;br&gt;
5a. The sides of a square are 16 cm in length. The midpoints of the sides of this square are joined to form a new square and four triangles. The process is repeated twice.
Let Xn denote the length of one of the equal sides of each new triangle.
Let An denote the area of each new triangle.
The following table gives the values of Xn and An, for 1 less than or equal to n less than or equal to 3.

N    1 2 3
Xn  8 __ 4
An 32 16 __

(First blank I got 6, second blank I got 8)   &lt;---  NO;  YES&lt;br&gt;

How did you get 6 for X2?  Xn is the length of a side of the triangle (short side, not the hypotenuse) at step n.&lt;br&gt;
The areas of the triangles go down by a factor of 2 each time.  That is (to me at least) clear from the diagram; it also agrees with your results showing A1=32, A2=16, and A3=8.&lt;br&gt;
The area of each triangle is one-half base times height, which in this problem is one-half the square of the length of the side.  So you should always have
{{{An = (1/2)(Xn)^2}}}&lt;br&gt;
If X2 is 6, then A2 would be
{{{(1/2)(6^2) = 18}}}
but we know it is 16.&lt;br&gt;&lt;br&gt;
5b. The process described above is repeated. Find A6.
A6 = 8&lt;br&gt;
You correctly found A3 to be 8, and the numbers are getting smaller, by a factor of 2 each time.  How can A6 be 8?
You know the areas are going down by a factor of 2 each time; if A3 is 8, what will A6 be?&lt;br&gt;&lt;br&gt;
5c. Consider an initial square of side length k cm. The process describes above is repeated indefinitely. The total area of the shaded regions is k cm^2. Find the value of k.&lt;br&gt;
For part C, there is nothing in the statement of the problem that defines which areas are shaded.&lt;br&gt;
I am guessing that the shaded areas are the areas of the triangles.  But with the process as described, if it is repeated indefinitely, then the whole original square ends up being shaded.&lt;br&gt;
If that is the right interpretation, then part C is asking for what value of k is the side length of the square in cm equal to the area of the square in square cm.  The answer to that is easy: k=1.</PRE>