2017 AMC 10A 第 3 题

Question

Tamara 的花园里有三排花坛，每排有两个

6

英尺乘

2

英尺的花坛。花坛之间以及花坛外侧都有

1

英尺宽的小路，如图所示。所有小路的总面积是多少平方英尺？

Tamara has three rows of two

6

-feet by

2

-feet flower beds in her garden. The beds are separated and also surrounded by

1

-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?

72

78

90

120

150

先求包括小路在内的整个矩形花园的尺寸。

Find the dimensions of the whole rectangular garden including walkways

用外部大矩形面积减去六个花坛的总面积。

Subtract the total area of the six flower beds from the outside rectangle

花园总宽为

2 \cdot 6 + 3 \cdot 1 = 15\text{，}

总高为

3 \cdot 2 + 4 \cdot 1 = 10\text{。}

因此花园总面积为

15 \cdot 10 = 150

。所有花坛的总面积为

6 \cdot 2 \cdot 6 = 72\text{。}

用花园面积减去花坛面积，得到小路面积

150 - 72 = 78

。

所以正确答案是 B。

We can see that the width of the garden is

2 \cdot 6 + 3 \cdot 1 = 15.

We can also see that the height is

3 \cdot 2 + 4 \cdot 1 = 10.

The total area of the garden is therefore

15 \cdot 10 = 150.

The area of all the flower beds is

6 \cdot 2 \cdot 6 = 72.

Subtracting this from the area of the garden yields

150 - 72 = 78,

which is the area of the walkways.

Thus, B is the correct answer.

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