AMC 8 1987 Problem 12

AMC8 1987 年第 12 题

面积与周长（综合）★★★☆☆

What fraction of the large 12 by 18 rectangular region is shaded?

着色部分占 12 × 18 大矩形区域的几分之几？

A. $\displaystyle \frac{1}{108}$
B. $\displaystyle \frac{1}{18}$
C. $\displaystyle \frac{1}{12}$
D. $\frac29$
E. $\frac13$

正确答案 · Correct Answer

解析 · Solution

Solution 1

The rectangle is divided into upper and lower halves, and then the lower half is divided into left and right halves. The lower right section is therefore

\displaystyle \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

of the area of the entire rectangle. Since this section is divided into 6 equal rectangles, 2 of which are shaded,

\displaystyle \frac{1}{3}

of the lower-right section is shaded, that is,

\displaystyle \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

of the large rectangle.

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