Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side . What fraction of the area of the octagon is shaded?

AMC 8 2015 Problem 2

AMC8 2015 年第 2 题

四边形与多边形★★☆☆☆

Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side \overlineAB. What fraction of the area of the octagon is shaded?

的中点，问在整个八边形面积中，图中阴影点 O 是正八边形 ABCDEFGH 的中心，X 是边𝐴𝐵 部分面积所占的比例是多少？

A. $\displaystyle \frac{11}{32} \quad$
B. $\displaystyle \frac{3}{8} \quad$
C. $\displaystyle \frac{13}{32} \quad$
D. $\displaystyle \frac{7}{16}\quad$
E. $\displaystyle \frac{15}{32}$

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