Octagon/Rectangle Area
Source:
January 5, 2009
geometryrectangle
Problem Statement
A regular octagon has an area of one square unit. What is the area of the rectangle ?
[asy]unitsize(8mm);
defaultpen(linewidth(.8pt)+fontsize(6pt));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,NNW);
label("",B,NNE);
label("",C,ENE);
label("",D,ESE);
label("",E,SSE);
label("",F,SSW);
label("",G,WSW);
label("",H,WNW);[/asy] (A)\ 1\minus{}\frac{\sqrt2}{2} \qquad
(B)\ \frac{\sqrt2}{4} \qquad
(C)\ \sqrt2\minus{}1 \qquad
(D)\ \frac12 \qquad
(E)\ \frac{1\plus{}\sqrt2}{4}