2006 AMC 10A Problems/Problem 7
Problem
Missing diagram
The 
rectangle 
is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is 
?
Solution
Since the two hexagons are going to be repositioned to form a square without overlap, the area will remain the same. The rectangle's area is 18*8=144. This means the square will have four sides of length 12. The only way to do this is shown below.
