2005 AMC 10A Problems/Problem 8
Problem
In the figure, the length of side of square is and =1. What is the area of the inner square ?
[asy] pair D = (0,0); pair C = (1,0); pair B = (1,1); pair A = (0,1); pair H = (0.25,0.6); pair E = foot(C,H,B); pair F = foot(D,C,E); pair G = foot(A,D,F); pair H2 = foot(B,A,G); draw(A--B--C--D--cycle,linewidth(1)); draw(B--H2,linewidth(1)); draw(C--E,linewidth(1)); draw(D--F,linewidth(1)); draw(A--G,linewidth(1)); label("",A,NW);label("",B,NE);label("",C,SE);label("",D,SW); label("",H2,SW);label("",G,SE);label("",F,NE);label("",E,NW);[/asy]