Problem
2013 AMC 8 Problem 24
Squares ABCD, EFGH, and GHIJ are equal in area. Points C and D are the midpoints of sides IH and HE, respectively. What is the ratio of the area of the shaded pentagon AJICB 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]](/static/aops/fba537995d130b17a771855c766afe6338cb3e41.png)
\textbf{(A)}\ \frac{1}{4}\qquad\textbf{(B)}\ \frac{7}{24}\qquad\textbf{(C)}\ \frac{1}{3}\qquad\textbf{(D)}\ \frac{3}{8}\qquad\textbf{(E)}\ \frac{5}{12}
Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.
Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)
Problem feedback
Difficulty
—