# Problem #1073

 1073 A regular octagon $ABCDEFGH$ has an area of one square unit. What is the area of the rectangle $ABEF$? $[asy] unitsize(10mm); defaultpen(linewidth(.8pt)+fontsize(8pt)); pair C=dir(22.5), B=dir(67.5), A=dir(112.5), H=dir(157.5), G=dir(202.5), F=dir(247.5), E=dir(292.5), D=dir(337.5); draw(A--B--C--D--E--F--G--H--cycle); label("A",A,NNW); label("B",B,NNE); label("C",C,ENE); label("D",D,ESE); label("E",E,SSE); label("F",F,SSW); label("G",G,WSW); label("H",H,WNW); [/asy]$ $\textbf{(A) } 1 - \frac{\sqrt{2}}{2} \qquad\textbf{(B) } \frac{\sqrt{2}}{4} \qquad\textbf{(C) } \sqrt{2} - 1 \qquad\textbf{(D) } \frac{1}{2} \qquad\textbf{(E) } \frac{1+\sqrt{2}}{4}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
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