1994 AMC 12 第 8 题

Question

在图示多边形中，每条边都与相邻的边垂直，并且全部

28

条边均全等。该多边形的周长为

56

。多边形所围区域的面积是

In the polygon shown, each side is perpendicular to its adjacent sides, and all

28

of the sides are congruent. The perimeter of the polygon is

56.

The area of the region bounded by the polygon is

84

96

100

112

196

每条边的长度是

\frac{56}{28}

Each side has length

\frac{56}{28}

以一条边长为单位，把图形分成宽度依次为

1,3,5,7,5,3,1

的水平条带

In units of one side length, split the shape into horizontal strips of widths

1,3,5,7,5,3,1

每条边长为

2

。以边长为单位，七个水平条带的宽度为

1,3,5,7,5,3,1\text{，}

总计

25

个单位正方形。每个正方形的面积为

2^2=4

，所以多边形的面积为

25\cdot4=100

。因此正确答案是 C。

Each side has length

2.

Measured in side-length units, the seven horizontal strips have widths

1,3,5,7,5,3,1,

totaling

25

unit squares. Each such square has area

2^2=4,

so the polygon’s area is

25\cdot4=100.

Thus the correct answer is C.

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