Difference between revisions of "2015 AMC 8 Problems/Problem 2"

Revision as of 14:24, 25 November 2015

Point $O$ is the center of the regular octagon $ABCDEFGH$ , and $X$ is the midpoint of the side $\overline{AB}.$ What fraction of the area of the octagon is shaded?

$\textbf{(A) }\frac{11}{32} \quad\textbf{(B) }\frac{3}{8} \quad\textbf{(C) }\frac{13}{32} \quad\textbf{(D) }\frac{7}{16}\quad \textbf{(E) }\frac{15}{32}$

@@ Line 2: / Line 2: @@
 <math>\textbf{(A) }\frac{11}{32} \quad\textbf{(B) }\frac{3}{8} \quad\textbf{(C) }\frac{13}{32} \quad\textbf{(D) }\frac{7}{16}\quad \textbf{(E) }\frac{15}{32}</math>
-[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("<math>A</math>",A,dir(45));
-dot("<math>B</math>",B,dir(90));
-dot("<math>C</math>",C,dir(135));
-dot("<math>D</math>",D,dir(180));
-dot("<math>E</math>",E,dir(-135));
-dot("<math>F</math>",F,dir(-90));
-dot("<math>G</math>",G,dir(-45));
-dot("<math>H</math>",H,dir(0));
-dot("<math>X</math>",X,dir(135/2));
-dot("<math>O</math>",O,dir(0));
-draw(E--O--X);
-[/asy]

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Difference between revisions of "2015 AMC 8 Problems/Problem 2"

Revision as of 14:24, 25 November 2015