2015 AMC 8 Problems/Problem 2
Revision as of 15:24, 25 November 2015 by Mathwizard888 (talk | contribs)
Point is the center of the regular octagon
, and
is the midpoint of the side
What fraction of the area of the octagon is shaded?
[asy] pair A,B,C,D,E,F,G,H,O,X; A=dir(45); B=dir(90); C=dir(135); D=dir(180); E=dir(-135); F=dir(-90); G=dir(-45); H=dir(0); O=(0,0); X=midpoint(A--B);
fill(X--B--C--D--E--O--cycle,rgb(0.75,0.75,0.75)); draw(A--B--C--D--E--F--G--H--cycle);
dot("",A,dir(45));
dot("
",B,dir(90));
dot("
",C,dir(135));
dot("
",D,dir(180));
dot("
",E,dir(-135));
dot("
",F,dir(-90));
dot("
",G,dir(-45));
dot("
",H,dir(0));
dot("
",X,dir(135/2));
dot("
",O,dir(0));
draw(E--O--X);
[/asy]