问题 解答题

在平面上,七个边长均为1的等边三角形,分别用①至⑦表示(如图).从④⑤⑥⑦组成的图形中,取出一个三角形,使剩下的图形经过一次平移,与①②③组成的图形拼成一个正六边形.

(1)你取出的是哪个三角形?写出平移的方向和平移的距离.

(2)将取出的三角形任意放置在拼成的正六边形所在平面上,问:正六边形没有被三角形盖住时面积能否等于?请说明理由.

答案

解:(1)当取出的是⑦时,将剩下的图形向上平移1(如图1);

当取出的是⑤时,将⑥⑦向上平移2(如图2);

(2)能.理由如下:

每个小等边三角形的面积为

五个小等边三角形的面积和为

正六边形的面积为

<<

所以正六边形没有被三角形盖住的面积能等于

图1

图2

问答题
阅读理解

阅读理解。

     Concern with money, and then more money, in order to buy the conveniences and luxuries of modern

life, has brought great changes to the lives of most Frenchmen. More people are working than ever before

in France. In the cities the traditional leisurely midday meal is disappearing. Offices, shops and factories are

discovering the great efficiency of a short lunch hour in company lunch rooms. In almost all lines of work

emphasis now falls on ever-increasing output. Thus the "typical" Frenchman produces more, earns more,

and buys more consumer goods than his counterpart of only a generation ago. He gains in creature comforts

and ease of life. What he loses to some extent is his sense of personal uniqueness, or individuality.

     Some say that France has been Americanized. This is because the United States is a world symbol of the

technological society and its consumer products. The so-called Americanization of France has its critics.

They fear that"assembly-line life" will lead to the disappearance of the pleasures of the more graceful and

leisurely(but less productive)old French style. What will happen, they ask, taste, elegance, and the cultivation

of the good things in life - to joy in the smell of a freshly picked apple, a stroll by the river, or just happy

hours of conversation in a local café?   

     Since the last 1950's life in France has indeed taken on qualities of rush,tension, and the pursuit of

material gain. Some of the strongest critics of the new way of life are the young, especially university

students. They are concerned with the future, and they fear that France is threatened by the triumph of this

competitive, goods-oriented culture. Occasionally, they have reacted against the trend with considerable

violence.   

     In spite of the critics, however, countless Frenchmen are committed to keeping France in the forefront

of the modern economic world. They find that the present life brings more rewards, conveniences, and

pleasures than that of the past. They believe that a modern, industrial France is preferable to the old.

1. Which of the following is a feature of the old French way of life?

A. Leisure, elegance, and efficiency.

B. Elegance, efficiency, and taste.

C. Leisure, elegance, and taste.

D. Efficiency, taste, and convenient.

2. Which of the following is NOT true about Frenchmen?

A. Many of them prefer the modern life style.

B. They actually enjoy working at the assembly line.

C. They are more concerned with money than before.

D. They are more competitive than the old generation.

3. The passage suggests that _____.

A. great changes have occurred in the life style of all Frenchmen

B. it's now unlikely to see a Frenchman enjoying a stroll by the river

C. the French are fed up with the smell of freshly picked apples

D. in pursuing material gains the French are suffering losses elsewhere

4. The main idea of the passage is "_____ ".

A. Changes in the French Way of Life

B. Criticism of the New Life Style

C. The Americanization of France

D. Features of the New Way of Life