2013/8/24/Three squares
Source:
November 27, 2013
ratiogeometryrectanglerotationAMC
Problem Statement
Squares , , and are equal in area. Points and are the midpoints of sides ad , 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);
dot("", A, NW);
dot("", B, NE);
dot("", C, NE);
dot("", D, NW);
dot("", E, NW);
dot("", F, SW);
dot("", G, S);
dot("", H, N);
dot("", I, NE);
dot("", J, SE);[/asy]