Difference between revisions of "2000 AMC 8 Problems/Problem 6"

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==Solution==
 
==Solution==
  
Square FECG¡ square FHIJ = <math>4 \times 4 - 3 \times 3 = 16 - 9 = \boxed{\text{(B)}} 7</math>.
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Square FECG¡ square FHIJ = <math>4 \times 4 - 3 \times 3 = 16 - 9 = \boxed{\text{(B) 7}}</math>.

Revision as of 09:17, 15 May 2011

Problem

Figure $ABCD$ is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded $L$-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]

$\text{(A)}\ 7 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 12.5 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 15$

Solution

Square FECG¡ square FHIJ = $4 \times 4 - 3 \times 3 = 16 - 9 = \boxed{\text{(B) 7}}$.