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

\overline{AB}

. What fraction of the area of the octagon is shaded?

点

O

是正八边形

ABCDEFGH

的中心，

X

是边

\overline{AB}

的中点。问在整个八边形面积中，图中阴影部分面积所占的比例是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Since octagon

ABCDEFGH

is a regular octagon, it is split into 8 equal parts, such as triangles

\bigtriangleup ABO, \bigtriangleup BCO, \bigtriangleup CDO

, etc. These parts, since they are all equal, are

\displaystyle \frac{1}{8}

of the octagon each. The shaded region consists of 3 of these equal parts plus half of another, so the fraction of the octagon that is shaded is

\displaystyle \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{16} = \frac{7}{16}

继续练习