2013 AMC 8 Problems/Problem 24

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?

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(E--I); 
draw(F--E); 
draw(I--J); 
draw(J--F); 
draw(G--H); 
draw(A--J); 
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);
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See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.