Difference between revisions of "2013 AMC 8 Problems/Problem 24"
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draw(A--B); | draw(A--B); | ||
draw(C--B); | draw(C--B); | ||
| − | draw(D--A); | + | draw(D--A); |
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draw(F--E); | draw(F--E); | ||
draw(I--J); | draw(I--J); | ||
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draw(A--J); | draw(A--J); | ||
filldraw(A--B--C--I--J--cycle,grey); | filldraw(A--B--C--I--J--cycle,grey); | ||
| + | draw(E--I); | ||
label("$A$", A, NW); | label("$A$", A, NW); | ||
label("$B$", B, NE); | label("$B$", B, NE); | ||
Revision as of 13:03, 27 November 2013
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?
![[asy] pair A,B,C,D,E,F,G,H,I,J; A = (0.5,2); B = (1.5,2); C = (1.5,1); D = (0.5,1); E = (0,1); F = (0,0); G = (1,0); H = (1,1); I = (2,1); J = (2,0); draw(A--B); draw(C--B); draw(D--A); draw(F--E); draw(I--J); draw(J--F); draw(G--H); draw(A--J); filldraw(A--B--C--I--J--cycle,grey); draw(E--I); label("$A$", A, NW); label("$B$", B, NE); label("$C$", C, NE); label("$D$", D, NW); label("$E$", E, NW); label("$F$", F, SW); label("$G$", G, S); label("$H$", H, N); label("$I$", I, NE); label("$J$", J, SE); [/asy]](http://latex.artofproblemsolving.com/f/b/a/fba537995d130b17a771855c766afe6338cb3e41.png)
Solution
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
