Difference between revisions of "2013 AMC 8 Problems/Problem 24"
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<asy> | <asy> | ||
pair A,B,C,D,E,F,G,H,I,J; | pair A,B,C,D,E,F,G,H,I,J; | ||
+ | |||
A = (0.5,2); | A = (0.5,2); | ||
B = (1.5,2); | B = (1.5,2); | ||
Line 18: | Line 19: | ||
draw(A--B); | draw(A--B); | ||
draw(C--B); | draw(C--B); | ||
− | draw(D--A); | + | draw(D--A); |
− | |||
draw(F--E); | draw(F--E); | ||
draw(I--J); | draw(I--J); | ||
Line 25: | Line 25: | ||
draw(G--H); | draw(G--H); | ||
draw(A--J); | draw(A--J); | ||
− | + | filldraw(A--B--C--I--J--cycle,grey); | |
− | + | draw(E--I); | |
− | + | dot("$A$", A, NW); | |
− | + | dot("$B$", B, NE); | |
− | + | dot("$C$", C, NE); | |
− | + | dot("$D$", D, NW); | |
− | + | dot("$E$", E, NW); | |
− | + | dot("$F$", F, SW); | |
− | + | dot("$G$", G, S); | |
− | + | dot("$H$", H, N); | |
+ | dot("$I$", I, NE); | ||
+ | dot("$J$", J, SE); | ||
</asy> | </asy> | ||
− | |||
− | |||
− | |||
− | |||
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Latest revision as of 09:59, 16 July 2024
Problem
Squares ,
, and
are equal in area. Points
and
are the midpoints of sides
and
, respectively. What is the ratio of the area of the shaded pentagon
to the sum of the areas of the three squares?