2000 AMC 8 Problems/Problem 6
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Problem
Figure 
is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded 
-shaped region is
![[asy] pair A,B,C,D; A = (5,5); B = (5,0); C = (0,0); D = (0,5); fill((0,0)--(0,4)--(1,4)--(1,1)--(4,1)--(4,0)--cycle,gray); draw(A--B--C--D--cycle); draw((4,0)--(4,4)--(0,4)); draw((1,5)--(1,1)--(5,1)); label("$A$",A,NE); label("$B$",B,SE); label("$C$",C,SW); label("$D$",D,NW); label("$1$",(1,4.5),E); label("$1$",(0.5,5),N); label("$3$",(1,2.5),E); label("$3$",(2.5,1),N); label("$1$",(4,0.5),E); label("$1$",(4.5,1),N); [/asy]](http://latex.artofproblemsolving.com/7/c/6/7c6ea431a00e38c9ba0b8513fa0b9a39252cfcef.png)
Solution
Square FECG¡ square FHIJ = 
.
